Bồi dưỡng học sinh giỏi vật lý 11 tập 1

NHONG CHO t KHI GIAI B A I T A F - Khi dp dung djnh luat Culong ve siT tU'dng tac giffa cdc dien tich dffng yen can chu y: + dieu kien ap dung: hai dien tich diem hoac hai qua cau tich

LQI NOIDAU

« B6I DlfONG HOC SINH GI61 VAT L I TRUNG HQC PHO THONG" la

bo sach dung cho hoc sinh kha gioi, hoc sinh cac Idp chuyen Vat l i , cac thay c6 giao

day Vat li d cac trUdng trung hoc pho thong Bo sach gom 7 cuon:

1 Boi dUdng hQC sinh gioi Vat U 10, tap I (Donf^ hoc, Dong lUc hoc, TTnh hoc)

2 Boi dUdng hpc sinh gioi Vqt li 10, tap I I (Cac dinh luat bcio loan, Nhiet hoc)

3 Boi dUdng hQC sinh gioi Vat li 11, t|ip I (D/pn va Dien til) •

4 Boi dUdng hgc sinh gioi Vat li 11, tap II (Quang hinh)

5 Boi dUdng hgc sinh gioi Vat li 12, tap I {Dao dong va Song ai hoc)

6 Boi dUdng IIQC sinh gioi Vat li 12, tap II {Dong dien xoay chieu va Dao don^

dien tCe)

7 Boi dUdng hgc sinh gioi Vat li 12, tap III {Quang li Vat li hat nhdn)

Ve cau true, moi cuon sach deu du'dc chia thanh cac phan Idn, trong moi phan

gom nhieu chuyen de, moi chuyen de la mot noi dung kien thiJc tron ven Moi

chuyen de gom cac phan:

A-T6m tat kien thrfc: Phan nay chiing toi trinh bay mot each c6 he thong

nhi^ng kien thiJc trong tam cua chuyen de tiif cd ban den nang cao trong do chiing toi

chu trong dao sau nhffng kien thiJc nang cao de lam cd sd cho viec giai cac bai tap

cua chuyen de

B-Nhi?ng chu y khi giai bai tap: Trong phan nay chiing toi neu len nhu'ng

chii y can thiet ve kien thiJc va ki nang giai bai tap Do la nhu'ng lufu y quan trpng

giiip dinh hu'dng va tranh nhu'ng sai sot khi giai cac bai tap cua chuyen de

C-Cac bai tap cua chuyen de: He tho'ng bai tap d day kha da dang du'dc s^p

xep ttf de den kho, tCf ddn gian den phiJc tap va di/dc giai kha chi tiet nen rat phii

hdp vdi nhieu do'i tU'dng ban doc

Trong qua trinh bien soan chiing toi tham khao rat nhieu nguon tai lieu trong

va ngoai niTdc, dac biet la cdc bo sach G/a/ loan Vat U do thay Biii Quang Han lam

chu bien - Nha xuat ban Giao due 1998, bo sach Bai tap va Un gidi Vat li do OS

Yung Kuo Lim lam chu bien - Nha xuat ban Giao due Viet Nam 2010, bo sach Ca

sd Vat li do David Halliday lam chu bien - Nha xuat ban Giao due 2002 de lam

phong phU them phan kien thiJc cung nhiTphan Idi giai cac bai tap trong bo sich

Vdi SLf gop siJc cua cac thay c6 giao da va dang cong tac tai cdc tnTdng

chuyen, cac thay c6 giao da tijfng tham gia boi difdng hoc sinh gioi Vat l i cua cac

tinh thanh trong ca ni/dc, hi vong bo sach se la tai lieu tham khao thie't thifc, bo ich

cho nhieu doi tifdng ban doc yeu thich bo mon Vat l i

Mac dil da dau tiT bien soan kha kl ludng nhiftig nhu'ng han che, sai sdt la dieu

khong the tranh khoi Rat mong nhan difdc sif dong gop, chia se cua cac thay c6

giao va cac em hoc sinh tren ca nifdc; Moi y kien dong gop xin gufi ve dia chi

ngphudong@gmail.com hoac khang vietbookstore@vahoo.com.vn

Xin tran trong gidi thi^u bo sach den quy thay c6 giao va cic em hoc sinh!

I Dien tich - S\i tifdng tac giffa cac di^n tich

1 Di^n tich: Cd hai loai dien tich: dien tich du'dng va dien tich am Cac dien tich cung loai thi day nhau, cac dien tich khac loai thi hut nhau

2 Djnh luat Culong: LiTc ti/dng tac giufa hai dien tich diem diJng yen ti le

thuan vdi tich dp Idn ciia hai dien tich va ti le nghjch vdi khoang each giiJa Chung

k l q£ 2 |

e' r^ xjflq •'•

+ e la h^ng so' dien moi ciia moi triTdng ( 8 = 1 : chan khong hoac khong khi)

+ r la khoang each giffa hai dien tich qi, q2

Chii y : Dinh luat Culong du'dc ap dung cho: / " ^ j ^f'^ ^ \

- hai dien tich diem ^

- hai qua cau tich dien phan bo deu i< " ^1

Trong mot he CO lap ve dien, tdng cac dien tich dtfdc bao toan:

q, + q2 + = const j „ ^t^, ^^,(^-,3

B NHONG CHO t KHI GIAI B A I T A F

- Khi dp dung djnh luat Culong ve siT tU'dng tac giffa cdc dien tich dffng yen can

chu y:

+ dieu kien ap dung: hai dien tich diem hoac hai qua cau tich dien phan bo deu

+ cac hien tU'dng thiTc te" thffdng gap:

• cho hai qua cau nho dan dien nhiT nhau da nhiem dien tiep xiic nhau hoac

no'i vdi nhau bKng doan day dan roi tdch rdi ra thi tdng dien tfch se chia deu cho hai qua cau: q'l = q'2 = ' '

• khi cham tay vao mot qua cau nho dan dien da tich dien thi qua cau se mat dien tich va trd thanh trung hoa

3

Bdi diiOng hgc sinh gi6i Vat ly 11, t$p 1 - Nguyin Phu D6ng

- Khi mot dien tich diem q chju tac dung ctia nhieu life tac dung Fp F j , do

cac dien tich diem qi, q2, gay ra thi hcJp life tac dung len q la:

-f De xac djnh do Idn cua hdp luTc F ta c6 the diTa vao: **

+ djnh l i ham cosin: F^ - Fj^ + F2 + 2FjF2Cosa (a la goc hdp bdi Fj va )

• F, va F2 cung chieu thi: F = F, + F2 (a = 0, cosa = 1) ^

• F, va F2 ngiTdc chieu thi: F = IF, - F2I (a = n, cosa = -1)

• F, va F2 vuong goc thi: F= ,JF^ + F^ (a = 90°, cosa = 0)

• Fj va F2 cung do Idn (Fi = F2) thi: F = 2Fi cos y

+ phiTdng phap hinh chieu: F = ^jF[+F^

(F, = F u + F2x + Fy = F,y + F2y + )

- Khi mot dien tich q du'ng yen thi help luTc tac dung len q se bang 0:

F = F, + F2 + = 6

-f Cac life tac dung len dien tich q thi/dng gap la:

+ trong life: P = mg (luon hu'dng xuong)

+ life tTnh dien: F = SiSl Q^^Q ne'u q, va q2 trai dau; \\ic day ne'u q,

Cty TNHH MTV DVVHUhang Vi?t

c C A C B A I T A P vi; Lye T U O N G T A C TITOI D I E N

1 Tl/CfNG T A C G I 0 A CAC D I E N T I C H D I E M DlfNG YfeN 1.1 Hai dien tich diem bang nhau dat trong chan khong, each nhau doan R = 4cm

Li/c day tTnh dien giffa chiing 1^ F = 10'^N

a) Tim do Idn moi dien tich

b) Tim khoang each R, giffa chiing de liTc day tTnh dien la F, = 2,5 lO^^N

Bai giai

a) Do Idn mSi dien tich

_ Vi: + Hai dien tich day nhau nen q, va q2 cung dau

+ Hai dien tich bang nhau nen: qi = q2 ' 1

- Theo dinh luat Cu-16ng:

F = k R^ R'

b) Tinh so electron dirtrong moi hat bui, biet dien tich moi electron la e = 1,6.10-"C

B6i diiBng hpc sinh gi6i Vjt ly 11, t?p 1 - IMguygn Phu B6ng

b) So electron diT trong moi hat bui

Smi v'c,fy ::r"!,; I

Vay: So' electron d\X trong moi hat bui la ne = 6.10^

1.3 Moi proton c6 khoi liTdng m = l,67.10""kg, dien tich q = 1,6.10""C Hoi life

day Culong giiya hai proton Idn hdn li/c hap dan giffa chiing bao nhieu Ian?

Bai giai

- L\ic day Cu-16ng giffa hai proton la: F = k =

k Lire hap dan giifa hai proton la: F ' = G m , m 2 = G m

= 1,35.10 ,36

Vay: Life day Cu-16ng giffa hai proton Idn hdn life hap dan giCfa chung

1,35.10^'' Ian

1.4 Hai vat nho giong nhau, moi vat thifa mot electron Tim kho'l lu'dng m6i vat

de life tlnh dien bang life hap dan

a) Tinh do Idn life hifdng tarn dat len electron

b) Tinh van toe va tan so'chuyen dong cua electron

Coi electron va hat nhan trong nguyen tur hidro tUdng tac theo djnh luat tTnh

dien

Cty TIMHH MTV U W H khang V i ^

Bai giai ^,, ,

a) Dp Idn life hU'dng tarn dat len electron

Vi life hU'dng tam trong chuyen dong tron cua electron quanh hat nhan chinh

la life tTnh dien nen:

F M = k ^1^2 = 9.10"

(-1,6.10~'^).1,6.10 ^-19

= 9,2.10-* N

R^ (5.10"")2

Vay: Do Idn life hU'dng tam dat len electron la: Fh, = 9,2.10"* N * " - ^

b) Van toe va tan so chuyen dong cua electron , ,

va n = 2,25.10^ « 0,71.10"/s

27tR 2.3,14.5.10'"

Vay: Van to'c va tan so' chuyen dong cija electron la Fh, « 2,25.lO' m/s va

n « 0,71.10"/s

1.6 Hai vat nho mang dien tich dat trong khong khi each nhau doan R = I m , day

nhau bang life F = 1,8N Dien tich to'ng cong cua hai vat la Q = 3.10"^C Tinh dien tich moi vat

- Theo dinh luat Cu-16ng, taed: F = k

1.7 Hai qua cau kim loai nho nhu nhau mang cac dien tich qi, q2 dat trong khong

khi each nhau R = 2cm, day nhau bang life F = 2,7.10^N Cho hai qua cau

Bdi diJ8ng hpc sinh gi6i Vjt ly 11, tap 1 - Nguyin Phu B6ng

tiep xiic nhau roi lai diTa ve vi tri cu, chiing day nhau bang lye F' = 3,6.10^N

Tinhqi,q2

Bai giai

- Khi hai qua cau chU'a tiep xuc, ta c6:

F = k FR^ ^2,7.10-^(2.10'^)^ k ~ 9.10^ = 12.10

=> qiq2 = 12.10'^ (1) (hai qua cau day nhau)

- Khi cho hai qua cau tiep xiic nhau roi tach ra xa nhau thi: F' = k q;q2 R^

2 H ; G TONG HglP TAG DyNG LEN MOT D l t N TIGH

1.8 Ba dien tich diem q, = -10"'C, q2 = 5.10"'C, = 4.10"'C Ian lu-dt dat tai A,

B, C trong khong khi, AB = Scm, AC = 4cm, BC = 1cm Tinh life tac dung len

moi dien tich , , ,

4.10"^5.10-.F2= 16,2.1 0"'N _ Lire tdc dung len qs: F3 = Fjj + F23 => F3 = F13 + F23 (F,3 ;F23 cung chieu)

1.9 Ba dien tich diem q, = 4.10"^C, q2 = -4.10"^C, q3 = 5.10"*C dat trong khong

khi tai ba dinh ABC cua mot tarn giac deu, canh a = 2cm Xac dinh vectd life tac dung len q3 , ; „,,:•< i s ^ j j ,

+ diem dat: tai C

+ phi/dng: song song vdi AB

+ chieu: tiTAdenB

+ doldtn:F3 = 45.10"^N _ i i

1.10 Ba dien tich diem qi = qj = q3 = q =

1,6.10""C dat trong chan khong tai ba dinh tarn giac deu canh a = 16cm Xac djnh lire tac dung len dien tich q3

Bai giai

Taco: F3 = F,, + F23, vdi

I1I3 Fi3 = k

F23 = k I2I3 a

a

B6i duBng hoc sinh gi6i V$t 1^ 11, tjp 1 - NguySn PhO Dflng

F,3 = F 2 3 va a = (F,3,F23) = 60° => F 3 = 2F,3Cos-^ = 2 k \0

^ F 3 = 2.9.10-/''^-'^7f.^ = 15,6.10-N

(i6.io"2)2 2 I r

Vay: Vectcf liTc tac dung len q3 c6:

+ diem dat: tai C

+ phu'dng; vuong gdc vdi AB

+ chieu: ra xa AB

+ do ldn:F3= 15,6.10-^'N

1.11 Ba dien tich diem qj = 27.10'^C, qj = 64.10"^C, q3 = -10"'C dat trong khong

khi tai ba dinh tam giac ABC vuong goc tai C Cho AC = 30cm, BC = 40cm

Xac dinh vectd liTc tac dung len q3

(4.10"')^ = 36.10^N

= > F 3 = >/F^TF^ = V(27.10-^)^+(36.10"^)^ =45.10'^N

Vay: Vectd liTc tac dung len q^ cd:

+ diem dat: tai C

+ phiTdng: CO (O la trung diem AB)

(tan OCB = _ 13 _ AC

F23 BC ) + chieu: tiT C den O

+ do Idn: F3 = 45.10"'N \ :

-1.12 Tai ba dinh tam giac deu canh a = 6cm trong khong khi cd dat ba dien tich

q, = 6.10'"C, q2 = q3 = - 8.10"'C Xac dinh liTc tac dung len qo = 8.10~'C tai

tam tam giac

Ann

+ diem dat: tai O

+ phiTdng: vuong gdc vdi BC \ + chieu: tij" A den BC

+ doldn:Fo = 8,4.10-^N " ^

1.13 Hai dien tich q, = 4.10'^C, q2 = -12,5.10"*C dat tai A, B trong khong khi,

AB = 4cm Xac dinh lire tac dung len qj = 2.10"'C dat tai C vdi CA 1 AB va

11

B6i clL0ng hpc sinh gi6i Vjt ly 11, tgp 1 - Nguygn Phd Dfing

+ diem dat: tai C - j

+ phU'cfng: hdp vdi A C mot goc P: cosP =

2F13F3

=> cosP = (8.10^'*)^ +(7,65.10"*)" -(9.10~^)2 « 0,34 => p « 70°

2.8.10"^7,65.10~^

+ dp l d n : F 3 = 7,65.1 O^N ^'-^ ' ' C - v t y , , V ' ' " '

1.14 C6 6 dien tich q b^ng nhau dat trong khong khi tai 6 dinh luc giac deu canh

a T i m lire tac dung len moi dien tich » |

B a i giai

Do tinh doi xiJng nen ta chi can khao sat mot dien tich ba't k i , ch^ng han dien

tich tai B tren hinh ve

Cty TNHH MTV DWH Khang Vi?t

Vay: LiTc tac dung len m 6 i dien tich c6:

+ diem dat: tai cac dien tich

+ phU'cfng: AvtUng thang noi dien tich tSm luc giac

+ chieu: ttr tarn luc giac ra

q2 (15 + 4^3) + do Idn: F = k-

12

1.15 Bon dien tich q giong nhau dat d 4 dinh tu" dien deu canh a T i m life tac

dung len moi dien tich

Vay: Life tdc dung len moi dien tich c6:

+ diem dat: tai cac dien tich ' '•u >

+ phiTcfng: hdp v d i mat tur dien mot g6c a: cosa ^ — —

2 F E 23

13

B6i du8ng hpc sinh gi6i V?t ly 11, tjp 1 - Nguygn Phu B6ng

1.16 ffinh lap phiTdng A B C D , A ' B ' C ' D ' canh a = 6.10"'°m dat trong chan khong,

Xac djnh life tac dung len moi dien tich, ne'u: •

a) Co 2 dien tich q , = q2 = 1,6.10-"C tai A, C; 2 dien tich qa = q4 = -1,6.10-"C

t a i B ' va D '

b) Co 4 dien tich q = 1,6.10""C va 4 dien tich - q dat xen ke nhau d 8 dinh cua

hinh lap phiTdng

Cty TNHH MTV DVVH Khang ViSt

TiTdng tir doi vdi cac dien tich q2, qs va q4

Vay: Do Idn liTc tac dung len m o i dien tich la F « 0,45.10"'N

B6i duSng hpc sinh gioi Vat ly 11, tgp 1 - IMguygn Phu D6ng

F l z = F2I(z) + F3i(z) + F4i(z) + Fri(z) + F2-l(z) + FS-KZ) + F4-i(z) ' > * M

- TiTdng tiT cho cac dien tich khac • >

VSy: Do Idn cua life dien tac dung len moi dien tich la F « 0,54.1 O - ' N

•fW •-'"n • , - ,1,/ ,|i •

3 SlJ C A N B A N G C U A D I E N T I C H ^''^

1.17 Hai dien tich q, = -2.10"^C, q2 = 1,8.10"^C dat trong khong khi tai A va B,

AB = / = 8cm Mot dien tich qa dat tai C Hoi:

a) C ct dau de q3 n^m can bhng?

b) Da'u va do Idn cua qs de qi, q2 cung can bang

* * B^igiai

a) V i tri cua C de qs nhm can b^ng

- Cac life dien tac dung len qs: Fjj.Fjj.'

- De q3 nkm can b i n g thi: F^J + F23 = 0 => Fjj = - F j j => Fjj.Fjj cung phu'dng,

ngifdc chieu va c&ng do Idn: Fo = F23 <=> k

Vay: De q, va qa cung can bang thi qj = +0,45.lO'^C

1.18 Tai ba dinh tarn giac deu, ngu'di ta dat 3 dien tich giong nhau qi = q2 = q3 =

q = 6.10~^C Phai dat dien tich thuf tUqo d dau, la bao nhieu de he can bang?

Bai giai

- Cac lire dien tac dung vao qo: FJQ , FJQ va FJQ

De qo can b^ng thi: F,Q + F2Q + FJQ = 0

V i qi = q2 = q3 = q = 6 lO^C => qo n^m d tarn

tarn giac ABC

- V i tinh doi xiJng cua he nen de he can bang ta

Ichi can xet them dieu kien can bang cua mot Itrong ba dien tich kia, chang han q3 De q3 can ^

Ib^ng thi: Fo3 + Fj3 + F23 = 6

Bfii dugng hpc sinh gi6i V^t ly 11, t^p 1 - NguySn PhCi B6ng

1.19 d moi dinh hinh vuong canh a c6 dat dien tich Q = lO'^C Xac dinh dau, dp

Idn dien tich q dat d tarn hinh vuong de ca he dien tich can bang?

Bai giai

- Vi dien tich d cac dinh hinh vuong nh\S nhau nen dien tich q dat d tarn hinh

vuong luon can bhng

- Vi he CO tinh doi xufng nen chi can xet dieu kien can b^ng cua mot trong cac

dien tich con lai, chdng han dien tich dat d D

- De dien tich dat d D nam can bang thi: Fj4 + F24+F34+Fq= 6

=:>F'4 + F24 = Fq ( F , 4 + F 3 4 - F 4 )

- De Q ct D n^m can bhng thi q < 0 q = -—(2yf2 + \)

4 Vay: De ca he can bang thi q = -^(2^/2 +1)

1.20 Hai qua cau kirn loai nho giong nhau moi qua c6 dien tich q khoi li/cfng

m = lOg, treo hd'i hai day ciing chieu dai / = 30cm vao ciing mot diem GiiJ

qua cau I co djnh theo phifdng th^ng diirng, day treo qua cau II se lech goc

a = 60" so vdi phiTdng thang diifng Cho g = lOm/sl Tim q

Bai giai

- Cac life tac dung len qua cau II: trpng life P ,

lUccSngday f va li/cdien F H

- Qua cau II nhm can bhng nen: P + f + F = 6

- Tarn giac liTc "gach gach" 1^ tarn gidc deu n6n: F = P P

IR, • •

CtyTNHH MW'DWHJ<h.ng Vi^t q2

hay k ^ = mg q = l 1^ V K mg = 3.10-^' 10"^10 = lO^C \^

Vay: Dien tich q = 10-*C ' "

1.21 Hai qua cau kim loai nho giong nhau treo vao mot diem bdi hai day / =

20cm Truyen cho hai qua cau dien tich tong cpng Q = 8.10"^C, chung day

nhau, cac day treo hdp thanh goc 2a = 90° Cho g = lOm/sl a) Tim khoi lu'dng moi qua cau

b) Truyen them cho mot qua cau dien tich q', hai qua cau van day nhau nhu'ng g6c giiJa 2 day treo giam con 60° Tinh q' '

Bai giai ;:';•;:! si

a) Khoi liTdng moi qua cau «

Ta c6: Kho'i lifdng moi qua cau la m; dien tich moi qua cau \k

Q 8.10 -7

= 4.10-'C

- Cac liTc tac dung len mot qua cau: trpng liTc P, liTc c^ng day T v^ life dien F

- Qua cau nam can bang nen: P + f + F = 6

- Suy ra: F = P t a n a o k ^ =mg.tan45°(r= l\/2)

=>m = (lV2)^g.tan45° 2l2g.tan45° kq^ kq^

-T\2

m = 9.10 (4.10'0 2.(2.10')^10.1

= l,8.10-\g=l,8g

Vay: Kho'i lu'dng cua moi qua cau la m = l,8g

b) Dien tich truyen them cho mot qua cau

- Khi truyen cho mot qua cau dien tich q' thi goc giffa hai qua cau giam nen q' < 0 Vi hai qua cau van day nhau nen (q + q') > 0

- Dien tich cua qua cau di/Pc truyen them dien tich la (q + q')

q.(q + q')

- ri^dngtiTcaua, t a c 6 : F ' = P t a n a ' o k = mg.tan30° (r' = 1}

q + q' mg.tan30°.l^ kq 1,8.10"^10.^.(2.10"')^ 9.10^.4.10 -7 = 1,15.10-'C '

19

B6i du8ng hoc sinh gioi Vat ly 11, t j p 1 - Nguygn Phu D6ng

V i q > 0 ; q ' <Onen: q' = 1,15.10'- 4.10'=-2,85.10 'C

Vay: Dien tich truyen them cho mot qua cau la q' =-2,85.10"^C

1.22 Hai qua cau nho bang kim loai giong nhau treo tren hai day dai vao cCing

mot diem, du'cfc tich dien bang nhau va each nhau doan a = 5cm Cham nhe

tay vao mot qua cau Tinh khoang each cua chung sau do

Bai giai

Goi q, m la dien tich ban dau va khoi liTcJng cua moi qua cau > , ? =T

- Trirdc khi cham tay vao mot qua cau, dieu kien can bang cua mot qua cau cho:

2 tana = - « — (F = k ^ ; P = mg)

Khi cham tay vao mot qua cau, qua cau do se ma't he't dien tich, life dien giiJa

hai qua cau khong con nffa, hai qua cau se cham vao nhau va dien tich lai

du'cfc phan bo deu cho hai qua cau (q' = ~ ) ' hai qua cau lai day nhau va

khoang each giiJa chiing la a', lu'dng tiT, tCf dieu kien can bang ciia mot qua

cau lijc nay ta suy ra:

Vay: Khoang each giffa hai qua cau sau khi cham tay la a' « 3,15cm '

1.23 Hai qua cau nho giong nhau khoi lu'dng rieng Di du'dc treo bang hai day

nhe Cling chieu dai vao cCing mot diem Cho 2 qua cau nhiem dien giong

nhau, chiing day nhau va cac day treo hdp goc a i Nhiing he vao chat dien

moi long cd khoi lUdng rieng D2, gdc giila 2 day treo la a2 < a i

a) Tinh e cua dien moi theo D i , D2, ai, a2

b) Dinh D, de aj = a, , ' ' i>? ^ " f

Bai giai , ,

a) Tinh e cua dien moi theo D i , D2, tti, a2

- Trong khong khi: ' •

Trong dien moi E:

+ Cac lire tac dung vao mot qua cau: trong lire P, li/c cSng day , lire dien F2 va lire day Ac-si-met F^

+ Dieu kien can bang cua mot qua cau cho:

a F2 = (P-FA)tan-

a •2 \2

= (D,-D2)Vg.tan (2) e(2/sin ?)

Vay: Gia tri cua D, de a, = aj la D, =

1-24 Hai dien tich q, = 2.10'^C va q2 = -8.10"'C dat tai A va B trong khong khi,

A B = 8cm Mot dien tich qa dat d C Hoi:

^) C 6 dau de q., can bang? Khi qj can bang, qj phai cd dau nhu" the nao de can bang nay la can bang ben? khong ben?

B6i dU3ng hoc sinh gi6i V$t ly 11, t$p 1 - Nguygn Phu D6n9

b) Oa'u va do Idn cua qj de he can bang? K h i he can hKng, tW can bang cua he

I ben hay khong ben?

B a i giai a) V i t r i cua C de q3 n ^ m can bang va dang can bang < " •

- V i t r i cua C • ,

+ Cac \\ic d i e n tac dung l e n qf F j j F j , ! ' '

+ D e q3 nam can bang thi: F , , + = 0 => F,3 = -F23 => Fi3,F23 cung phiTdng,

ngiTdc chieu va cung dp Idn: F o = F23 o k

C AC^ B C '

hirdng du^a t r d ve vj tri

can bang cu nen day la

can bang ben

+ N e u q3 > 0: K h i diTa q3 lech

k h o i vj t r i can b^ng thi hdp

lire ( F j 3 + F 2 3 ) se CO xu

hu^dng diTa q^ ra xa vj t r i

can bang cu nen day la

can bhng khong ben

V a y : Phai dat q3 tai C, v d i A C = 8cm; B C = 16cm thi q3 se nam can bang va

can bang do la can bang ben hay khong ben tuy thuoc vao da'u cua q3

b) Da'u va do \dn cua q3 de q i , q2 cung can bang, dang can bhng cua he

- Da'u va do Idn cua q3 de he can bang

+ D e q , va q2 cung can bang thi: F21 + F 3 , = 0 va F,2 +F32 - 0 => F21 = F3,

ben nen can bang cua he la can bang ben

V a y : D e q i va q2 cQng can bang thi q^ = -8.10'^C va can bhng cua he la can

bang ben , , ,

1.25 Co 3 qua cau cung k h o i lu^dng m = lOg treo b^ng 3 sdi day manh cCing chieu dai / = 5cm vao cung mot d i e m O K h i tich cho m o i qua cau d i e n tich q , Chung day nhau, each nhau doan a = 3 V 3 cm T i m q ? Cho g = 1 Om/sl

B a i giai

- K h i ba qua cau each nhau mot doan a => he can bang V i he do'i xi?ng nen chi

• can xet m o t qua cau, chang han qua cau tai C

- V d i qua cau tai C:

+ Cac lire tac dung l e n qua cau: cac lire d i e n F,3,F23; trong lire P3 va liTc

cang day T 3

+ Qua cau can bang nen: F j j + F23 + P3 + 73 = 6 => F3 + P3 + = 0

=>F'3 = P3tana, v d i P 3 = mg;F'3 = 2F,3Cos30° = 2 k 3 - — = V s k ^ Vik- = mg.tana

- Tarn giac O G C cho: tan a = GC

,2 2 (1)

B6i duSng hoc sinh gi6i Vgt ly 11, tjp 1 - IMguygn Phu D6ng

= a mga = 3 ^ 3 10^1 0,01.10.373.10"^

3.9.10% ( 5 1 0 - ^ ) ^ - ^ ^ : ' ? " > !

.10'^ = 1,14.10^C

• fjiiVi-.'sri'fiCr

V a y : D i e n tich cua m o i qua cau la q = ± 1,14.10"^C

1,26 M o t vong d a y ban kinh R = 5cm tich dien Q phan bo d e u tren vong, vong

dat trong mat phang thang diJng Qua cau nho m = I g tich dien q = Q diTdc

treo bKng mot day manh each dien vao diem cao nha't cua vong day K h i can

bang, qua cau nam tren true cua vong day Chieu dai cua day treo qua cau la

/ = 7,2cm, tinh Q

B a i giai

- Cac lire tac dung len qua cau: trong liTc P ; life dien F ; liTc cang day T

- Qua cau nam can bang nen: P + F + T = 0

P - - ,

- Tarn giac lU'c "gach gach" cho: F = , v d i : F = I d F (tong cac liTc dien

tana cua cac phan tuf nho cua vong day tac dung len q)

kq

P = mg; F = ZdF.eosa = ZdQ.cosa=

I ' kQ' m g

—-^.cosa =

kQ^ mg

sma

tana mgl

R (sina = y )

V a y : D i e n tich cua vong day la Q = ± 9 IO"*C

1.27 Hai qua cau nho cung khoi \\idng m, du'dc tich dien giong nhau q Chiing

du'dc no'i v d i nhau bang mot 16 x o nhe each dien, chieu dai tif nhien cua lo xo la /o, dp ciJng k ' M o t sdi chi, each dien, manh, nhe khong dan, c6 chieu dai 2 L , m o i dau day ehi dUdc gan vdi mot qua cau Cho d i e m giffa

O cua sdi day chi chuyen dong thang duTng hu'dng l e n vcti gia toe a , c6 dp Idn bang ^ (g gia toe rPi tif do)

L6 xo C O chieu dai / ( 2 L >l> lo) nhuThinh ve Xac dinh gia trj cua q?

B a i giai na, vrs-it 'nu' -i' ;

V i he C O tinh doi xifng nen ta ehi can xet mot qua cau, chang han qua cau

ben phai (hinh ve):

Cac liTc tac dung l e n qua cau: trong life P ; life dien F ; liTc d a n hoi F , ; life

quan tinh F^ ; liTc cang day T _ Qua cau nam can bang nen: P + F + Fj + F + T = 0 (1) _ T i r ( l ) s u y r a : F - F, = (P + F;,)tana '•^isl , - i ^ ^ g W i (2)

k ^ k ' ( / / o ) = (mg + m | ) 1^

V a y : D i e n tich cua m o i qua cau la = 1 3mgl + 2 k ' ( l - l o )

A T O M T A T K I E N T H i r C

I Di^ntrirt/ng '

1 Di^n t r i f t f n g : D i e n triTdng sinh ra bdi dien tich Q la viing khong gian ton

tai xung quanh dien tich Q va tac dung liTc dien l e n dien tich khdc dat trong no

2 CiftJfng dp dipn trvliing: CiTdng dp dien

tn/5ng do dien tich d i e m Q gay ra tai d i e m

M each Q mot doan r eo:

+ D i e m dat: T a i M + Phu-Png: Dirdng thang noi Q va M + Chieu: HiTdng ra xa Q neu Q > 0; hiTdng ve Q neu Q < 0

Bfii dUSng hpc sinh gidi Vat ly 11 tjp 1 - Nguygn Phu Dong

3 MO'i quan h$ giffa ctfcfng do di§n trUcfng Itfc d i ^ n trtfcfng: Khi dat dien

tich thur q trong dien trong dien truf&ng E thi q se chju tac dung ciia life

dien trUtJng F , v d i : " j ' " i - - i • u

+ C h i e u : q > 0 : F , E cung chieu; q < 0: F , E ngiTOcchieu *

+ Do Idn: F = IqlE :

-4 Nguyen l i chong cha't di$n trtftfng: Neu trong M E ,

khong gian c6 nhieu dien tich diem Q i , Q2, thi

dien trUdng tdng h d p do cac dien tich nay gay ra

tai diem M each Q i , Q2, Ian lUdt la r i , Vj, la:

E = E , + E 2 + E

11. D i n h h' Ostrogradski - Gauss

1. D i ^ n t h o n g : D i e n thong (thong liTdng dien

tru'dng) qua dien tich S la dai lu'dng xac dinh bdi:

N = ES.cosa ( a la goc hdp bdi vectd E va phap

'{ tuyen n cua dien tich S )

2. D j n h If Ostrogradski - Gauss; Dien thong qua mat kin c6 gia trj b a n g

tong dai so' cac dien tich c6 mat ben trong mat do chia cho SQ :

N = — E q ; = 47iklq; , ; - vf^'-"".: • ^'

^0

B NHtJNQ CHU Y KHI GlAl BAI TAP

- Can phan biet giffa yeu cau " t i n h " va "xac d i n h " cffdng dp dien trffdng: tinh

(tinh do Idn), xac dinh (ca diem dat, phffdng, chieu va dp Idn)

- Khi bieu dien vectd cffdng dp dien trffdng do mot dien tich diem gay ra can

chu y den dau cua dien tich: Q>0 ( E hudng xa Q ) , Q<0 ( E hiTdng ve Q)

Cong thUiC tinh cffdng dp dien triTdng do dien tich diem gay ra cung di/dc

dung de tinh cffdng dp dien trffdng do mot qua cau tich dien phan bo deu gay

ra vdi r la khoang e a c h tCr tam qua cau den diem ta xet

- Trffdng hdp c6 nhieu dien tich diem Q i , Q2, gay ra tai diem M cac ciTdng

dp dien trffdng E,, E 2 t h i ta dung nguyen l i chong cha't dien trffdng de xac

dinh cirdng dp dien triTdng tong hdp tai M De tinh dp Idn ciTdng dp dien

trffdng tong hdp tai M can chii y cac trUdng hdp dac biet sau:

+ Neu Ep E 2 Cling chieu thi E = Ej + E2

+ Neu E j , E 2 ngi/dc chieu thi E = IE, - E2I

+ Neu E p § 2 vuong goc thi E = ^E^+E^

Cty TNHH MTV DVVH Khang Vi^t

dien trffdng do vat do gay ra ta c6 the dung mot trong hai each sau:

+ Cac/i 7: Phi^cJng phap vi phan: ^ '

• Chia vat thanh nhieu vat raft nho, moi vat nho do dffdc coi nhiT mot dien tich diem. rJy->'y^r 'ii','' • ••' •

• Cffdng dp dien trffdng do vat gay ra la tong hdp cua cffdng dp dien triTdng

do nhieu vat ra't nho (dien tich diem) gay ra: E = l A E j

• TCf tinh doi xilng cua vat ta xac dinh dffdc hufdng va dp Idn cua E

+ Cdch 2: Phu'dng phap dung dinh l i 0 - G :

• Tinh dien thong: N = ES.cosa (a la goc hdp bdi hiTdng cua E va hffdng

phap tuyen n ciia S)

2.1 Qua cau bang kim loai, ban kinh R = 5cm dffdc tich dien diTdng q, phan bo deu

T a dat a = la mat dp dien mat (S: dien tich mat cau)

s Cho a = 8,84.10''' C/ml Hay tinh dp Idn cua ciTdng dp dien triTdng tai diem each be mat qua cau doan 5cm

B a i giai Chpn mat Gauss la mat cau S' dong tam vdi qua cau, ban kinh r = 10cm

~ Dien thong qua m a t s ' l a : N = ES'.cos a = E S ' = E 4 7 I T ^

~ Theo dinh li 0 - G ta cd: N = 4rtklqi = 47tkoS = 47ika.47tR^ = 167r^R^ka

=>E 47cr2 = 167r^R2ko=>E= 4 7 i k ( - ) ^ a

=>E = 4.3,14.9.10^(—)^8,85.10-^ = 2,5.lOW/m

10

-27 •

B6i duBng hpc sinh gi6i Vjt ly 11, tjp 1 - Nguy§n Phu D6ng

Vay: Dp Idn cua cUdng dp dien trUdng tai diem each be mat qua ciu doan

5cmla E = 2,6.1 OW/m

2.2 Proton dirpcdat vao dien tru'dngdeuE= 1,7.1 OV/m ,•

a) Tinh gia toe cua proton, biet mp = 1,7.10 "kg

b) Tinh van toe proton sau khi di dU'pe doan du'dng 20cm (van toe dau bang

Vay: Gia toe eiia proton trong dien tru'dng la a = 1,6.10''* m/s^

b) Van toe proton sau khi di dU'pe doan du'dng 20cm

Taco: v 2- V ( ^ = 2 a s =^ v = ^v^ + 2as = +2.1,6.10''*.0,2 =8.10^m/s

Vay: Van toe proton sau khi di dU'pe doan du'dng 20cm la v = 8.10'' m/s

2.3 Electron dang chuyen dpng vdi van toe VQ = 4.10^m/s thi di vao mot dien

trU'cJng deu, cUdng dp dien tru'dng E = 910 V/m, V Q eilng chieu diTdng siJc

dien tru'dng Tinh gia toe va quang du'dng electron chuyen dpng cham dan

deu CLing chieu du'dng siJe Mo ta chuyen dpng ciia eleetron sau do

Bai giai

^ ! V i electron mang dien tich am nen life dien tru'dng F tac dung len electron

se ngu'de chieu vdi chieu dien tru'dng E nghla la ngu'dc chieu vdi chieu

, chuyen dpng cua electron nen electron se chuyen dpng cham dan deu, cung

chieu vdi chieu du'dng sdc dien tru'dng vdi gia toe:

- Sau khi diTng lai, dU'di tac dung cua liTc dien tru'dng, electron se thu gia toe a'

(a' = -a = l,6.10'Ws^) va chuyen dpng nhanh dan deu theo chieu ngiTdc lai

(ngu'de chieu vdi dien tru'dng)

2. S\J CHONG C H A T DIEN TRl/OlNG - DIEN T I C H CAN BANG TRONG

D I E N TRUOfNG

2.4 Cho hai dien tich q, = 4 1 0 ' ° C , qz = ^ l O ' ^ C dat d A, B trong khong khi,

AB = a = 2em Xac dinh vectd eiTdng dp dien tru'dng E tai:

28 , ,

a) H, trung diem A B

M each A 1cm, each B 3em

c) N hdp vdi A, B thanh tarn giac deu i ' '

+ diem dat: tai H ^ + phu'dng: du'dng thang A B

+ chieu: ttj" A den B (eung chieu vdi E, va E^)

+ dp Idn: E H = 72.10'V/m

b) Vectd cu'dng dp dien triTdng tai diem M

Taco: E^=E^+E^

- V i A M = AB + B M = > M nam tren diTdng thang AB, ngoai doan AB, ve phia A

- V i E , ngi/dc chieu vdi E2 nen EM = | E I - E J

.= 9.10' ,-10

, - 2 x 2 = 4.10'V/m

(3.10"^)

= 32.10' V/m Vay: Vectd cu'dng dp d i e n triTdng tai M c6:

+ phufdng: diTdng thang A B

rV 01} ,

E M M E^ A + chieu: hiTdng ra xa A (eung chieu vdi E , do Ei > E2)

+ dp Idn: EM = 32.10'V/m

c) Vectd eirdng dp dien trUdng tai diem N V ' o i M - ' ' 1

Taed: E N = E , + E 2 s«:^>5,n,} n

- e

Bfii duBng hoc sinh gidi Vat ly 11, tjp 1 - Nguygn Phu D6ng

+ diem dat: tai N

+ phi/Png: dirdng thang A B

+ chieu: tiT A den B

+ dp Idn: E N = 9 1 0 ' V / m

2.5. Cho hai dien tich qi = q2 = 4.10"'°C dat d A, B trong khong k h i , A B = a =

2cm Xac dinh vectP ciTdng dp dien triTdng E tai: ,

TT = 0 ( 1 0 - ' ) ' A H E, B Vay: VeetP cu'dng dp dien tru'dng tai H c6 dp Idn bang 0

b) Vectd eirdng dp dien tru'dng tai diem M

T a c d : E j ^ = E, + E 2

- V i A M = A B + B M = > M nlm tren diTdng thang AB, ngoai doan A B , ve phia A

- V i Ej Cling chieu vdi E2 nen E M = E I + E2

Vectd eirdng dp dien tru'dng tai diem N

( 2 1 0 " ' ) ' 2 Vay: Vectd cu'dng dp dien tru'dng tai N eo:

+ diem dat: tai N

+ phu'dng: vuong goe vdi A B + chieu: hu'dng ra xa A B + dp Idn: E N * 15,6.10^ V/m

2.6. Hai dien tich qi = S.IO'^C, qj = -S.IO^^C dat tai A, B trong khong k h i , A B = 4cra T i m vectd cu'dng dp dien tru'dng tai C tren trung triTc A B , each A B 2em, suy ra life tac dung len q = 2 1 0 ' C dat d C

1+ d i e m dat: tai C

i+ phi/dng: song song vdi A B

chieu: tijf A den B

It dp Idn: E c = 9^2.10^ (V/m)

= 9>^.10^(V/m)

31

BoiduSng hoc sinh gioi Vat ly 11, tap 1 - Mguyen Phi'i Dong

- D o Idn life tac dung len q dat tai C:

Fc = Ec = 2 1 0 ' ' 9^.\0^ » 2 5 , 4 1 0 " ' N

Vay: Life tac dung len dien tich q dat tai C c6:

+ diem dat: tai C

+ phU'dng: song song vdi A B ' '

+ chieu: cting chieu vdi E,; (do q > 0)

+ do Idn: Fc « 25,4 l O ^ N

2.7 Hai dien tich q, = -IQ-'^C, q2 = lO^C dat tai A, B trong khong k h i , A B = 6cm

Xac dinh vectd E tai M tren trung triTc A B , each A B = 4cm

M A ^

(5.10"^)^ 5

= 0,432.10^ V/m

Vay: Cifdng do dien tri/dng tai diem M c6:

+ diem dat: tai M

+ phi/dng: song song vdi A B

+ chieu: ttr B den A

+ do Idn: E M = 0,432.10'V/m ' ® ^

2.8 Tai 3 dinh tarn giac A B C vuong tai A canh a = 50cm, b = 40cm, c = 30cm

Ta dat cac dien tich q, = q2 = qj = 10"'C Xac dinh E tai H , H la chan difdng

- D o Idn cua ct/dng do dien tru'dng tai H :

Ej ~i~ ^2 ^ 3 — Ej ~i~ E2'^ •

Vay: D o Idn cu^dng do dien tru'dng tai H la E H = 246 V/m

2.9 Cho bo'n dien tich cdng do Idn q dat tai bon dinh hinh vuong canh a T i m E

tai tarn O hinh vuong trong tru'dng hdp bo'n dien tich Ian liTdt cd dau sau:

Vay: Tru'dng hdp dau cua cac dien tich Ian li/dt la + + + + thi Eo = 0

b) Tru'dng hdp dau cua cac dien tich Ian liTdt la + - + - : :\

E Q = Ej + E2 + E 3 + E^ = E,3 + E24 => Eo = 0 Vay: Tru'dng hdp dau cua cdc dien tich Ian lu'dt la + - + - thi Eo = 0

c) Trufdng hdp dau cua cac dien tich Ian liTdt la + - - +:

33

B6i duSng hgc sinh gi6i V$t ly 11 tjp 1 - IMguy§n Phu D6nq

2.10 Tai ba dinii A, B, C ciia hinh vuong ABCD canh a dat 3 di^n tich q giong

nhau (q > 0 ) Tinh E tai:

' a) Tarn O hinh vuong , , b ) D i n h D

a b) CifcJng do dien triTcJng tai dinh D

Vay: CircJng do dien trirdng tai dinh D la E D = ( \ / 2 + - ) ^

2.11 Hai dien tich qi = q > 0 va q2 = - q dat tai A , B trong khong khi Cho A B = 2a

a) Xac dinh ciTdng do dien tru'dng E M tai M tren trung triTc cua A B , cdch A B

doan h

b) Xac djnh h de E M dat ciTc dai Tinh gid tri ciTc dai nay

Bai giai

a) CiTcJng do dien trUdng E M tai M tren trung trifc cua A B

Cty TNHH MTV DWH Khang Vi$t

2.12 Tai ba dinh ABC cua tu" dien deu SABC canh a trong chan khong c6 ba

dien tich diem q giong nhau (q < 0) Tinh do Idn cu'dng do dien tri/cJng tai dinh

S cua tu" dien Xac dinh hiTdng cua cu'dng do dien tru'dng nay

Bai giai ,

Ta c6: E^ = Ej + E j + E3 = E, + E23

- VI q, = q2 = q3 = q < 0; r i = rz = r3 = a nen El = E2 = E 3 = k ^

- VI a = (Ej.Ej) = 60° nen t ulri;:;, B ( v > '

E23 = 2E2Cos30° = 2 k W : / l = Vik 4 ' '

a^

2-E23 n\m tren duTdng cao SH cua tam giac SBC

Suy ra: E^ = E^ + E23 + 2EjE23Cosp, , - ;

v<3i cosp = S H ^ + S A ^ - A H ^

2SA.SH

35

Bi5i du3ng hpc sinh gi6i Vat ly 11, tjp 1 - Nguyin Phu Bfing

.Es= A / 6 - va E 5 hiTdng ve tarn tam giac ABC

Vay: VecW ciTdng do dien triTdng tai dinh S cua tu" dien c6:

2.14 Cho hai dien tich diem qi va q2 dat d A, B trong khong khi, AB = 100cm

Tim diem C tai do ciTdng do dien triTdng tdng hdp bang khong vdi:

a) qi = 36.10-^C; q2 = 4.10-^C b) q, = -36.10-'C; q2 = 4.10-*C

Bai giai

+ hirdng: tiT S den O (ban doc tiT chUng minh!)

2.13 Hinh lap phiTdng A B C D A ' B ' C ' D ' canh a trong chan khong Hai dien ticii

Qi = q2 = q > 0 dat d A, C; hai dien tich qj = q4 = - q dat 6 B ' , D ' Tinh do Idn

curdng do dien triTdng tai tam O hinh lap phiTdng

B6i du3ng hqc sinh gidi vat ly 11, t?p 1 - NguySn Phu D6n9

2.15 Cho hai dien tich q,, q2 dat tai A va B, A B = 2cm Biet q, + q2 = 7.10^^C va

diem C each qi 6cm, each qa 8cm c6 ciTdng do dien triTcJng E = 0 T i m qi,

Vay: Gia trj cac dien tich q,, q2 la q, = -9.10^^C va = 16.10"*C

2.16 Cho hinh vuong A B C D , tai A va C dat cac dien tich q, = qj = q H o i phai

dat d B dien tich bao nhieu de curing do dien tru'dng d D bkng khong?

B a i giai

- Cu'dng do dien tru'dng do qi, gay ra tai D la: E j j = Ej + E 3

V i q, = q3 = q; A D = CD = a nen E.j = 2EiCOs45° *

khong

2.17. Mot hon bi nho bang kirn loai dU'cIc dat trong dau Bi c6 the tich V = 10mm\

khoi lU'cfng m = 9.10"'kg Dau c6 khoi liTcfng rieng D = 800kg/m\t ca difdc dat

trong mot dien tru'dng deu, E hudng thang duTng tif tren xuong, E =

4,1.10^V/ni-T i m dien tich cua bi de no can bang Id lijfng trong dau Cho g = lOm/s^

Cty TNHH MTV DWH Khann Vi$t

B a i giai

Cdc lyc tdc dung len hon bi: ,

+ Trong li/c P = mg (hi/dng xuo'ng) 1 + Lire day A c - s i - m e t F ^ - - D V g (hiTdng len) + Li/c dien tru-dng: F = qE (hiTdng xuong neu q > 0; hiTdng len neu q < 0)

Hai qud cau nho A va B mang nhiJng dien tich Ian lUdt 2.10^'C va 2 1 0 ' C diTdc treo d dau hai sdi day td each dien dai bang nhau Hai diem treo day M v^ N cdch nhau 2cm; khi can bang, vj tri cac day treo c6 dang nhi/ hinh ve Hoi

-de du'a c-de day treo trd ve vj tri thang dufng ngu'di ta phai dung mot dien tru'dng deu c6 hufdng n i o va do Idn bao nhieu?

B a i giai

- De diTa cac day treo trd ve vj tri thang dilng can phai tac dung liTc dien tru'dng ngUdc chieu vdi liTc tmh dien va ciing do Idn vdi

lire tinh dien: F ' = F , ,5;

VI q, < 0 nen E ngiTdc chieu vdi F nghla la cilng chieu vdi F (hirdng tuf

^ai sang phai)

Vdi qua cdu B: TiTdng tir ^ \

^%r. De dira cac day treo trd ve vi tri th^ng diJng can phai dung mot dien trirdng deu c6 hiTdng tCr trai sang phai va cd do Idn E = 4,5.10" V/m

39

Bfli duang hoc sinh gi6i Vjtt 1^ 11, tjp 1 - Nguygn Phu B6ng

3. Cl/dNG D O D I E N TRl/OfNG D O V^T MANG D I E N CO KICK THl/OfC

TAORA

2.19 Mot ban phang rat Idn dat thang dilng, tich dien deu vdi mat dp dien mat a,

a) Xac djnh E do mat phang gay ra tai diem each mat phang doan h Neu dac

diem cua dien truTdng nay ^

b) Mot qua cau nho kho'i lUdng m dien tich q cung dau vdi mat phang, diTcfc treo

vao mot diem co djnh gan mat phang bang day nhe khong dan, chieu dai /

Coi q khong anh hu'dng den sif phan bo' dien tich tren mat phang va khi can

, bang day treo nghieng goc a vdi phu'dng thang di^ng Tinh q

Bai giai

a) Cu'dng do dien tru'dng do ban phang gay ra *

Chon mat Gauss la hinh tru c6 dudng sinh vuong g6c vdti day, hai day hinh

tron CO dien tich S va each deu ban phang doan h

- Dien thong qua mat Gauss: N = Nj + N2

+ Phan dien thong qua mat ben: N| = ZEiAScosai = 0 (vl cosai = 0)

+ Phan dien thong qua hai day: N2 = SEiAScosa2 = 2ES

Vay: Cu'dng do dien tru'dng do mat phang gay

ra tai diem each mat ph^ng doan h:

+ la dien triTctng deu, c6 hu'dng vuong goc

vdi vdi ban phang, c6 do Idn E =

ta xet den ban ph^ng

b) Tinh dien tich q

- Cac life tac dung len q: trong life P, liTc dien

tru'dng F, liTc cang day f

- Tam giac liTc cho: tana = — = mg 2mgeo

Vdi q > 0

40

Cty TNHH MTV DWH Khang Vi$t

2mg£o.tana

Vay: Dp Idn cua dien tich q la 2mgSQ.tana

2 20 Tinh ciTdng dp dien tru'dng gay bdi 2 mat phang rpng v6 han:

a) Dat song song, mat dp dien mat a > 0 va -a

b) Hdp vdi nhau goc a va c6 ciing mat dp dien mat CT > 0

Bai giai ' Si'H'- ^ ' i ^ ^

a) Tri^ng hdp hai mat phang dat song song • Vdi mot mat phang: Chpn mat Gauss la hinh tru c6 dtfdng sinh vuong goc vdi

-ddy, hai day hinh tron c6 dien tich S va each deu ban phang doan h

+ Dien thong qua mat Gauss: N = ZEiAScosa2 = 2EiS < , • + Theo dinh li Ostrogradski - Gaus:

N = - I q i

=> 2E,S = —laAS = — CT.2S

28, = E2

+ +

-1 h

-1

+ +

B6\g hgc sinh gi6i Vjt ly 11, tgp 1 - Nguygn Phu P6ng

2.12 Mot ban phang rong v6 han dMc tich dien va dat vao mot didn tri/cfng deu

Biet cifdng do dien triTdng tong hOp d ben trii vh ben phai cua ban \h Ei, E2

hufdng vuong goc vdi ban, dp Idn Ei vh E2 Hay tinh mat dp dien mat a ciia

ban va life dien tac dung len mot ddn vj dien tich ciia b^n )f»n **

a) Mat d6 dien mat cua bin ph^ng lJ4 ^4k(»:'

Chpn mat Gauss la hinh tru c6 di/dng sinh vu6ng gdc vdi day, hai day hinh

tron cd dien tich S va each deu ban ph^ng doan h

- Dien thong qua mat Gauss: N = Ni + N2

sf + Phan dien thong qua mat ben: Nj = ZEiAScosai = 0 (vi cosai = 0) ' '

+ Phan dien thong qua hai day: N2 = Z E i A S c o s a 2 = E i S + E2S = ( E i + E 2 ) S

Vay: Mat dp dien mat a cua ban la a = eo(Ei + E2)

b) LiTc dien tac dung len mot ddn vj dien tich cua ban

(mat dp dien dai X) tai diem each day doan r

B a i g i a i

Chpn mat Gauss la hinh tru dong true vdi day, hai ddy hinh tron c6 hin kinh

r, chieu cao/ r e

Dien thong qua mat Gauss: N = Ni + N2 / • I : /

+ Phan dien thong qua hai day: N| =i;EiASeosai = 0(vicosai = 0)

+ Phan dien thong qua mat ben: N2 = ZE,AScosa,2= ES = E.27tr/

^ N = E.7tr/

42*

Cty TNHH MTV DWH Khang Vi$t

Theo dinh H Ostrogradski - Gaus:

2.23 Hai day dan thing dai v6 han dat song song trong khong khi cich nhau

doan a, tich dien cung da'u vdi mat dp dien dai X

a) Xae dinh E tai mot diem trong mat phlng doi xiJng giffa hai day, each mat phang chufa hai day doan h

b) Tinh h de E ciTc dai va tinh gia trj cure dai nay ''*'

I i I

I / I 27ieor r ^ ^ r ^

(h^ + ^-) 4 TriTdng hdp X >0 Vay: Ci/dng dp dien trUdng tai mot diem trong mat phing doi xtfng giffa hai day, each mat phing ehiJa hai day doan h la E = ^

4

b) Gia tri cua h de E eifc dai

43

B6i duSng hgc sinh gi6i Vgt ly 11, tgp 1 - Nguygn Phii D6ng

2.24 Qua cau ban k i n h R tich d i e n deu v d i mat do d i e n k h o i p va dat trong

khong k h i T i n h ciTdng do dien tri/dng tai d i e m each tam qua cau doan r

(trong va ngoai qua cau)

B a i g l a i

T a c 6 :

+ Du'dng sijrc dien triTdng la nhiTng du'dng thang hudng doc theo ban kinh qua cau

+ D p Idn ciTdng dp d i e n tru'dng tai cac d i e m nam tren cCing mat cau c6 gia tri

nhiT nhau

Chpn mat Gauss la mat cau dong tam v d i qua cau tich d i e n :

- D i e m M n a m ben trong qua cau: r i < R:

+ D i e n thong qua mat cau S , (ban kinh r , ) la: N = E S i = E 4nrj^

+ Theo dinh l i Ostrogradski - Gauss: N = —Zqi

+ D i e n thong qua mat cau S2 (ban kinh T2) la: N = E S 2 = E 4 ^ 2

+ Theo dinh l i Ostrogradski - Gauss: N = — Zq,

Cty TNHH MTV DWH Khang Vi?t

V a y : Cu:dng dp d i e n truTdng tai d i e m each tam qua cau doan r k h i r < R la

3

E ^ ^ ; k h i r > R la E =

38

2 25 Ben trong mot qua cau mang dien vdi mat dp dien khoi p c6 mot I 6 hong hinh

c l u Xac dinh dien tru'dng tai mot diem bat k i cua lo hong trong triTdng hdp: a) L o hong c6 cung tam v d i qua cau

w T a m Or cua qua cau each tam O2 ciia 16 hong mot khoang d

B a i g i a i a) Tru'dng hdp lo hong c6 ciing tam v d i qua cau _ G p i Ej la ciTdng dp d i e n triTdng do qua cau dac (khong c6 lo hong), mat dp dien k h o i p gay ra t a i d i e m M ; E j la ciTdng dp d i e n tru'dng do qua cau dac (c6 kich thUdc bang

lo hong), mat dp d i e n k h o i - p gay ra t a i

d i e m M Theo nguyen l i chong chat d i e n tri/dng, ta c6: E,^ = Ej + E j

- Theo ke't qua bai tren, ta c6: Ej = - ^ f ; E j

b) Tru'dng hdp tam O i cua qua cau each tam O2 cua lo hong mot khoang d

- Tirpng tir, ta c6: E , = — r j ; = ( r , = O ^ ; ^ = O^M)

B6\g hpc sinh gi6i Vat ly 11 tjp 1 - Mguyen Pliu Dony

Vay: Khi tam O i cua qua cau each tarn O2 cua I6 hong mot khoang d thi

CO chieu tuf O, den O2 va c6 do Idn EM = — '•' ' ' •

2.26 Mot v6 cau ban kinh trong Ri, ban kinh ngoai R2 mang dien tich Q phan bo

deu theo the tich Tinh cU'dng do dien trU'cJng tai ncfi each tam qua cau doan r

1 Di^n the': Dien the tai diem M trong dien triTdng dSc triTng cho dien

tru'dng ve mat diT trCT nSng liTdng va diTcfc do b^ng thiTdng so' giffa cong de

diTa mot dien tich q tuf diem M ra xa v6 ciTc va di$n tich q: V M =

2 Hi^u di^n th6': Hieu dien the giCTa hai di^m M v^ N trong di6n tnrdng dSc

triTng cho kha nSng thiTc hien cong cua dien trifcfng giffa hai diem d6 va

diTdc do b^ng thi/dng so giffa cong cua life dien lam di chuyen mot dien

tich q tit diem M den diem N va do Idn cua dien tich q:

A^^, _ A

Cty TNHH MTV DWH Khang Vi$t

3, Di?n tM' gSy ra hdi cac di$n tich diem

k Q

_ Dien the f^dy ra bdi mot dien tich diem Q:W=—.— ( = 0)

e r (r la khoang each tijf dien tich diem Q den diem ta xet)

_ Dien the f^dy ra bdi h$ di$n tich diem Q,, Q2, Goi V i , V2, la dien the

do cac dien tich Q], Q2, gay ra tai diem M trong dien trUdng Dien the toan phan do he dien tich tren gay ra tai M la: •' I V ' '

V = V , + V 2 + = SVj ; V i •••11 „

He thurc tren la npi dung cua nguyen 11 chong cha't dien th6'

4 LiSn gii?a cifofng dO di^'n trift/ng va hi$u di$n thfi' ,

M , N la hai diem tren cCing mot diTdng siJc;

E la ci/dng do dien tru'dng cua dien triTdng deu; d la khoang cdch giffa hai diem doc ^ — = ^ theo mot di/cfng suTc c6 hieu dien the la U ^ ^

I L T h ^ ' n a n g t l n h di$n The nang cua dien tich q dat tai diem M trong dien tru'dng dac tri/ng cho kha nang sinh cong cua dien triTdng khi dat dien tich q tai M :

- Lire dien triTcJng 1^ life th6' nen cong cfla liTc dien

trufdng khong phu thuoc vao dang quy dao di ^ , -^-'/f

chuyen cua dien tich ma chi phu thuoc vao vi tri cua diem dau va diem cuo'i cfla quy dao: A = qU

~ Mo'i quan he giila cong ciia liTc ngoai A ' v^ cong ^ M cua lire dien trircJng A: A ' = - A = - q U

•~ Doi vdi vat dan can b^ng di6n can chij ^:

+ Vat dan la vat d^ng the: Cdc diem ben trong vk trdn mat vat dSn c6 c&ng , dien the

+ Di?n tich chi phan bo 6 mat ngoai vat dan, tap trung 3 nhffng ch5 loi va nhon

- The nang tUdng tdc cua h? dien tich diem: V d i h? g6m cdc dien tich di^m Q i ,

Q 2 , - , the nang ciia h? la:

- N '

B6i dugng hpc sinh gi6i vat ly 11, tap 1 - Nguygn Phu D6ng

+ Trirdng hdp he 2 dien tich: W = - ( Q , V , + Q2V2), vdi V, = , V2 =

+ Trirdng hdp he 3 dien tich: W = - ( Q i V i + Q2V2 + Q 3 V 3 ) , vdi

kQ, k Q , kQ, kQ, kQ, k Q ,

C C A C B A I T A P V £ D I E N T H ^ - H I E U D I E N T H ^

1 CONG C U A LVC D I E N - D I E N T H E , H I E U D I E N T H E

3.1 Hieu dien the giOfa hai diem M , N trong dien triTdng U M N = lOOV

a) Tinh cong cua liTc dien trU'dng khi mot electron di chuyen tiT M de'n N

b) Tinh cong can thiet de di chuyen electron tCr M den N

b) Cong can thiet de di chuyen electron tiT M den N: A = - A = 1,6.10"''' J

3.2 De di chuyen q = lO^C tif rat xa vao diem M ciia dien trU'dng, can thirc hien

cong A ' = 5.10"'j Tim dien the d M (goc dien the d 00 )

Bai giai

Ta cd: Cong can thirc hien: A = - A = -q( - ) = -10^(0 - V M ) = 5.10"^ J

Vay: Dien the d diem M la V M = 0,5V

3.3 Khi bay qua 2 diem M va N trong dien trirdng, electron t5ng toe, dong nSng

tang them 250eV ( l e V = Ue.lO"'"^;) Tinh hieu dien the giffa M va N

VSy: Hieu dien the'giu'a hai diem M va N trong dien trirdng la U M N = -250V

3 4 Electron chuyen dong khong van toe dau tCf A den B trong dien trU'dng deu,

U B A = 45,5V Tim van toe electron tai B ^ U J , s

• Bai giai ' IM- - :;J I f i l ; ^

mv^

Ta cd: Cong cua lire dien trirdng: A = q U ^ = AW^ = ( U A B = - U B A = ^ 5 , 5 V )

2 ( - l , 6 1 0 " - ) ( - 4 5 ^ ^ ^ ^ , ^ ^ ^ ^ ^ ^ _ 9,1.10"^'

m VSy: VSn toe cua electron tai B la V B = 4.10^ (m/s)

3.5 Electron chuyen dong quanh nhan nguyen tuT hidro theo quy dao trdn ban

kinhR = 5.10-''em

a) Tinh dien the tai mot diem tren quy dao electron

b) Khi electron chuyen dong, dien trU'dng cua hat nhan cd sinh ra cong khong? Tai sao?

3.6 Dien tich Q = 5.10'C dat d O trong khong khi

a) Can thiTc hien A ' , bao nhieu de diTa q = 4.10^C tiT M each Q doan r i = 40em den N each Q doan r2 = 25cm

^) C i n thiTc hien cong A'2 bao nhieu de du'a q tijf M chuyen dong cham ra xa v6

B6i duSng hgc sinh gi6i Vat ly 11, tjp 1 - Nguygn Phu D6n9

+ Dien the tai diem N : = k — ^ = = 180V

^ 8.r2 0,25

- C6ng can thiTc hien de diTa q tuT M den N: A ' , = - A = - q U M N = - q ( V M - V N )

= ^ A ' , = - 4 1 0 " \ 12,5-180) = 2,7.10^J

Vay: Cong can thiTc hien de diTa q tuf M den N la A ' , = 2,7.10'*^;

b) Cong can thiTc hien de diTa q tCr M ra v6 Cling , ,

T a c 6 : V ^ = 0

=> A ' = - A = - q U ^ ^ = - q ( V ^ - V J = - q V ^ ' " '

A'2 = -4.10'.112,5 =-4,5.10"^ J

Vay: Cong can thiTc hien de diTa q tCr M ra v6 cung la A'2 = -4,5.10"^ J

3.7 Tinh the' nang cua he thong hai dien tich diem qi, q2 each nhau khoang r

trong chan khong

Bui giai Taco: + Dien the do qi gay ra: V = k —

r , + The nang cua he dien tich qi, q2: W = q2V = ^^^^

Vay: The nang cua he dien tich q,,q2 la W =

3.8 Hai dien tich q, = 2.10'^C, qj = -3.10"^C each nhau 20cm trong khong khi. Di

chuyen hai dien tich de chiing each nhau 50cm Nang li/dng cua he hai dien

tich tang hay giam Tinh do bie'n thien n^ng lu'dng cua he

Cty TNHH MTV DVVH Khang Vigt

E)6 bien thien nang liTcfng cua he:

= W2 - W, =-0,108 + 0,27 = 0,162 J > 0 : nang lu-dng ciia he tang

Vay: Khi di chuyen hai dien tich ra xa nhau thi nang liTdng cua he tang

3 9 Co the tich dien cho vao mot vat dan c6 lap den mot dien the toi da la bao

nhieu khi chieu vao vat mot chiim tia electron, bay vdi van toe v? Khoi liTcJng

jn va dien tich e cua electron coi nhUda he't

2e

3.10 Electron d each proton doan r = 5,2.10"'cm Muo'n electron thoat khoi siJc

hut proton no can c6 van toe toi thieu la bao nhieu?

3.11 Trong nguyen tO" hidro, electron chuyen dpng quanh hat nhan theo quy dao

tron ban kinh R = 5.10~'cm Tinh nang li/dng can cung cap de ion hoa nguyen tur hidro (du'a electron ra xa v6 cifc)

Bai giai Electron chuyen dong xung quanh hat nhan theo quy dao tron du'di tac dung

cua lire hu-dng tam, life nay chinh la liTe Cu-16ng

mr Dpng nang ciia electron: W = —mv^ = — 1 , 1 ke^ ke^ m-

2 2 mr 2r

W\g hQC sinh gi5i Vgt ly 11, t$p 1 - Nguyjn Phu D6rig"

- Nang lUdng can thie't de ion hoa nguyen tuf hidro: W = - W =

W = ^ • " ' ' • " • ' ^ • " ' " ' ^ 2 , 3 I O - ' - J 1 4 4 e V ;

2.5.10"*'

Vay: Nang liTdng can thiet de ion hoa nguyen lit hidro la W = 14,4 eV

3.12 Hai electron ban dau d rat xa nhau, chuyen dong l a i gan nhau Tinh

khoang each nho nhaft giiJa chiing trong cac triTcfng hdp sau:

a) Electron I du'cJc g i i l c6' dinh, electron I I bay den electron I vdi van toe dau VQ

b) Hai electron tiT do, chuyen dong ve phia nhau vdi ciing van to'c dau Vo

c) Hai electron tif do, ban dau electron I dilng yen, electron I I bay den electron I

vdi van to'c dau VQ

B a i giai

Chon go'c the nang d oo (V^ = 0 )

a) K h i electron I dUdc giff co dinh, electron I I bay den vdi van toe dau Vo

- Nang lu'dng cua he luc dau la dong nang cua electron I I : Wj^u = — ^ „

- Nang lu'dng cua he liic sau (khi diTng lai) la the nang tiTdng tac tmh dien tao

nen do siT c6 mat cua electron nay trong dien tru'dng tao hdi electron kia:

thi khoang each nho nhaft giffa chung la r = •

2ke^

m v j b) Khi hai electron tif do chuyen dong ve phia nhau

- Nang lu'dng cua he liic dau la dong nang cu^ hai electron:

Nang lu'dng cua he luc dau bang dong nSng ciia electron I I : Wd^,, = mv:

_ Nang lu'dng cua he luc sau: Ws,„, = mv ke^ mv^ - + • 2 k e '

Tinh van tdc qua cau khi den C Dinh a de qua cau cd the den dffdc C

B a i giai Chpn mdc the nang hafp dan d chan mat phang •'jjs r";)'!*) ,<!

nghieng; mdc the nang dien d vo cijng +q B iNang Iffdng cua dien tich +q gom co:

+ Dong nang: ^^^^

+ The' nang hafp dan: mgz + The'nang dien: Mz5):3 = _ kq^

-q A

B6i du3ng hpc sinh gi6i Vjt ly 11, tjp 1 - Nguyjn Phu B6ng

- Nang liTdng cua +q khi d B : WB = 0 + mgh + — ~ (1)

3.14 Hai dien tich q, = S.IO^^C va q2 = 2.10"^C dat tai 2 dinh A , D cua hinh chO

nhat ABCD, AB = a = 30cm, A D = b = 40cm Tinh:

b) Cong cua dien tru'dng khi q = lO'^C di chuyen tii" B den C , ,

Vay: Cong cua dien triTdng khi dien tich q di chuyen tCr B den C la A = 3,6.10

Cty TNHH MTV DWH Khang Vigt

3 15 Hai dien tich q, = 10~*C, q2 = 4.10"*C dat each nhau 12cm trong khong khi

Tinh dien the tai diem c6 cu"dng do dien triTcfng bing 0:

' B a i giai •' ''A i

Vi qi, q2 cung dau nen diem c6 ciTdng dp dien tru"dng bang 0 nam giiya qi, q2

Goi A la diem dat dien tich qi, B la diem dat dien tich qa, C la diem c6 cU"6ng (Jp dien trufdng bang 0, ta c6: Ec = El + E2 = 0

' AC^ BC^ AC^ (0,12-AC)2 (0.12-AC)^ 0 , 1 2 - A C J - - 'rrv.: , :

3.16 Hai dien tich q, = 3 lO^C, qj = -5 lO^C dat tai A, B trong khong khi, AB =

8cm Tim nhiJng diem c6 dien the bang 0:

a) T r e n A B i b) Tren du-dng vuong goc vdi AB tai A ^' ^* ' '

B6\g hpc sinh gi6i vat ly 11, t$p 1 - Nguygn Phu Dflng

Mat khac: B P ' - P A ' = A B ' = 64

=> B P ' - 0,36BP' = 64 => B P ' 100

= 5 > B P = 10 cm va A P = 6cm

Vay: Diem c6 dien the' bang 0 tren difdng

; vuong goc vdi A B tai A la P vdi B P = 10 cm A - © B

3,17 Hai dien tich diem q va -nq (n > 1) dat tai A , B each nhau doan a ChiJng

minh rang mat c6 dien the bang 0 la mat cau Tinh ban kinh R cua mat cau

va vj tri tam O cQa mat cau Ap dung vdi n = 2, a = 6cm ' ' A ! :

ij,,:' \;, • • •iv, , Bai giai

- Dien the do q gay ra tai khoang each rj: Vj = — '' *

- Dien the' do (-nq) gay ra tai khoang cAch T2: V, = "^^

- Gpi M la diem c6 dien the bang 0, ta c6: Vj^ = ^ - = 0

<=> kq _ nkq

- Chon goc toa dp O cua true Ox tai vi tri dat dien tich q thi dien tich (-nq) c6

toa dp a, diem M CO toa dp X, nen ta c6:

- Ket hpp (1), (2), (3), ta tha'y mat c6 dien the bang 0 la mat cau c^t true Ox tai

hai diem c6 toa dp va — ^ ; c6 dudng kinh la:

, a a

d === + •

' 1 + n 2na

n +1 n - 1 - 1

1-n hay CO ban kinh: R = —= •

2 n ^ - l

Cty TNHH MTV DWH Khang Vi^t

1-n Goi O la vj tri tam cua mat cau, ta c6: GO = R -

V a y Mat CO dien the bang 0 la mat cau c6 ban kinh R = , tam O' nam

tren di/c(ng thang A B , ngoai doan AB, each A doan 0 0 ' =

n ^ - l

3.18 Tai 3 dinh tam giac deu ABC canh a = 6\/^cm trong khong khi, Ian lu'dt

dat 3 dien tich diem q, = - l O ^ C , qz = qs = 10"^C Tinh:

a) Dien the tai tam O va tai trung diem M cua canh AB

b) Cong can de di ehuyen dien tich q = -10 '^C tCf O den M

B a i g l a l l o r f j i : - : r>

a) Dien the'tai tam O va tai trung diem M cua AB

f Dien the tai tam O: = ^ + ^ + ^ = - ^ ( q j + q 2 + q 3 )

b) Cong can de di chuyen q tuf O de'n M I'"01 <

Bfii dugng hpc sinh gi6i Vgt l» 11, tjp 1 - Nguyin Phii B6ng

Vay: Dien the tai tam hinh vuong la Vo = -9000 V

3.20 Ba dien tich diem q, = = qj = q = lO^C ban dau d ra't xa nhau Tinh cong

can thiTc hien de diTa 3 dien tich de'n 3 dinh cua tam giac deu ABC canh a =

3cm dat trong khong khi

Bai giai

Chon goc dien the tai v6 cung: = 0 Gia suT ban dau q, diJng yen cf A

- Cong can thiTc hien de du'a dien tich qj tijr oo de'n dinh B cua tam giac:

• : , „ ( i )

a' a" • qi

- Cong can thiTc hien de du'a dien tich q3 tijr oo de'n ;i,.<y^

dinh C cua tam giac: A3 = qjVs = qVs t 1

_ k q ^ k q 2 _ 2 k q

vdi: V3 = V , + V 2 = — ^ +

- Cong can thiTc hien de diTa ca ba dien tich tren den ba dinh A , B va C cua

tam giac la: A = A ^ A3 = ^ + ^ = ^ = ^.9.X0\iX0-^f ^ ^

a a a 3.10-2 Vay: Cong can thiTc hien de diTa 3 dien tich de'n 3 dinh ciia tam giac deu la:

A = 9.10-'J

3.21 Chiang minh rhng the nang ciia he n dien tich diem trong khong khi la

W , = ^ k ^ ( v d i i < j )

Bai giai

- Cong cua lire tac dung len vat trong trirdng liTc the bang dp giam the nSng

cua vat do trong triTcJng liTc, cong ma lire dien triTdng thi/c hien khi mot di?n

tich qdich chuyen tir A t d i B la: AAB = W A - W B ' v * '

Cty TNHH MTV DVVH Khang Vi^t

( W A W B : the nang cua dien tich q tai vi tri A , B )

Taco: W ^ = k ^ + C ; W ^ ^ ^ k ^ + C (Cla hhng so'tuy y)

The nang cua mot dien tich q, dat trong dien trircfng cua dien tich diem q2 v^

each dien tich nay mot doan r la: W = k + C 4 , ^ , J '

The nang cua he n dien tich diem trong khong khi: •

-i -i ^-i-i

3.22 Ba electron ban dau diJng yen d ba dinh tam gidc deu canh a, sau do chiing

chuyen dpng do li/c tirpng tac tlnh dien Tim van toe cuTc dai moi electron dat diTpc

Bai giai m m?,'r

- Tirdng tir bai 8.25 cong lufc dien trirdng de dira ca ba electron ra xa nhau

( W , , = Wd,„ax; W , = 0 nen V = v,„ax) la: A ' = A =

Vay: Van toe c\ic dai ma moi electron dat dirpc la v„,ax = e J— •

3.23 Hai dien tich +9q va - q dirpc giCT chat tai A, B trong chan khong, AB = a

M6t hat kho'i lirpng m, dien tich q chuye'n dpng doc theo diTdng AB nhir hinh ben Tim van to'c cua m khi d rat xa A, B d l no c6 the' chuyg'n dpng den B

59

B6i diOng hgc sinh gifli Vjt ly 11, tjp 1 - Nguygn Phu D6ng

Bai giai

Goi qi = 9q; q2 = -q; qa = q la dien tich chuyen dong doc theo AB: q3 chiu tac

dung cua liTc day cua qi, life hut cua q2

- Xet tai diem C each B khoang x, khi do ta c6: I

VI Fi3 > F23 nen life tdng hdp tac dung len q31^ li/c day, do do khi each

B mot doan ^ > — thi q3 se chuyen dong cham dan

+ Khi Fi3 = F23 =^ X = XQ = - : lire tonghdp tac dung len qjbkngO

j + Khi F,3 < F23 ^ X < - : liTc tdng hdp tac dung len qj la life hut

Nhir vay, van toe ban dau VQ toi thieu cua hat la iJng vdi van toe Vc cua hat

tai C bhng 0 (vc = 0)

- Ap dung dinh luat bao toan nang lu'cJng:

+ 6 xa v6 Cling hat ehi c6 dong nang: Wj = -^mv^

" + Tai C, VI Vc = 0 nen hat ehi c6 the' nang dien tru'dng ciia qi, qa:

+ Theo djnh luat bao toan n3ng liTcJng: Wj = Wc

Cty TIMHH MTV DVVHKhang Vi?t

3 24 Hai hat proton va hai hat pozitron ban dau nam yen xen ke nhau d cac dinh

cfla mot hinh vuong, sau do bay ra xa nhau Biet ti so khdi liTdng cua chiing —

m

- 2000, con dien tich thi gidng nhau Coi rang khi bat dau chuyen dong tu do,

cac hat pozitron se bay ra xa v6 eiTe ra't nhanh, sau do cac proton mdi tach xa nhau Tinh ti so van tdc pozitron va proton khi da bay xa nhau v6 ciTc

Bai giai <

]\lh^n xet: Ban dau, liTc tac dung len cac hat eo dp Idn bing nhau nhu^ng

M = 2000 nen cac hat pozitron c6 gia tdc Idn hdn gia toe cdc hat proton

m

2000 Ian Do do, cac hat pozitron se di ra xa v6 ciTc rat nhanh sau do cac hat

proton se tach ra do tiTdng tac giOfa chiing vdi nhau Vi the ta c6 the coi r^ng khi cac pozitron djch chuyen thi cac proton diJng yen ' •

Neu khong cd cac hat proton thi the nang tufpng tac giila cac hat pozitron la:

W = eV = ke^

Dien the do moi hat proton gay ra tai vi tri moi hat pozitron la:

v = ke The'nSng toan phan cua cac hat pozitron la:

Wo = W + 2eV' + 2eV' = ke^ 4ke^ a72

ke^

.^2 + 4

Khi cdc hat pozitron chuyen dnr^ rat xa nhau, to^n bp the nSng nay

chuyen thanh dong nSng c u; c lu.ig: Wo = W,,

B'fll difflng hoc slnh' g76i vgriyTTrrgtrT^'-wgiiyen vm uow

3.25 Vong day tron bdn kinh R tich dien deu vdi dien tich Q Tinh dien the tai

M tren true vong day, each tarn mot doan h

Bai giai

- Chia vong day thanh nhffng doan v6 ciing nho

di mang dien tich dq coi nhU' dien tich diem

Dien the tai M tren true vong day do d, gay ra:

3.26 Vong day ban kinh R tich dien Q phan bo deu, dat trong khong khi Dien

tich diem q cung da'u vdi Q tif A tren true vong chuyen dong den tam B cua

vong, AB = d Tim van toe nho nhat cua q tai A de q vUdt qua di/dc vong day

Kho'i li/dng q la m f " • '

Bai giai

Ta c6: Van toe nho nhat cua q tai A de q viTdt qua vong day tiTdng iJng viin

toe d B cua q se b&ng 0

- Nang li/dng cua q tai A: W A = k-,=2i== + ^^

- N a n g l i r d n g c u a q t a i B : W B = k ^ ( v i h = 0 ; v B = 0)

62

Cty TNHH MTV DWH Khahg Vijt

Ap dung dinh luat bao loan nang lUdng:

2 D I ? N T H E C U A V A T D A N T I C H D H 1 : N

3.27 Hai qua cau kim loai nho c6 ban kinh Ri = 3R2 dat each nhau doan r = 2cm trong khong khi, hut nhau bang liTc F = 27.10"^N Noi hai qua cau b l n g day

dan Khi bo day noi chiing day nhau bang \\ic F ' = 6,75.10'"'N Tim dien tich

liic dau cua cac qua cau ,

QUI quong hgc Sinn gioi vgt ly n , t j p 1 - Nguyen pnu uong

3.28 Co n giot thuy ngan hinh cau giong nhau dU'cJc tich dien, dien the' be mat

moi qua cau la VQ Nhap cac giot nay thanh mot giot hinh cau Idn Tim dien

the' tren mat giot Idn nay

Bai giai

•' '' kq

- Dien the be mat cua mot giot thuy ngan nho (ban kinh r) la: VQ = —

r

- Didn the be mat cua giot thuy ngan Idn (ban kinh R) la: V =

- Mat khac, the tich cua giot thuy ngan Idn bang the tich cua n giot thuy ngan

3 L I E N H E G I L T A Cl/CfNG D Q D I E N T R I / C K N G V A H I $ U D I E N T H E

3.29 Tam giac ABC vuong tai A dufdc dat trong ^

dien tnrdng deu , a = ABC = 60°; AB // E,

Bie'tBC = 6cm, U B C = 120V

a) Tim UAC, UBA va cUdng do dien triTdng EQ

b) Dat them d C dien tich diem q = 9.\0-^°C

Tim ci/dng do dien triTdng tdng hdp d A

a) Tinh UAC, UBA va EQ

- Hieu dien the giiTa hai diem A, C:

UAC = qEo.A'C' = 0

I

Cty TNHH MTV DWH Khann Vi$t

Hieu dien the giffa hai diem B, A:

U3;, = qEo.B'A' = U B c = 1 2 0 V Cifdng dp dien triTdng EQ:

Vay: Hieu dien the giiJa hai diem AC la UAC = 0; hieu dien the giuTa hai diem

BA la UBA = 120V; cufdng do dien tri/dng EQ = 4000 V/m

b) CUdng dp dien trifdng long hdp tai A Ci/dng dp dien trndng do q gay ra d A:

3.30 Dien tich q = 10"^C di chuyen dpc theo cac

canh cua tam giac deu ABC canh a = 10cm ^

trong dien trufdng deu cu"dng dp dien triTdng la: ^T^—V

E = 300V/m, E // BC Tinh cpng cua liTc dien B ' - - - ^ c trirdng khi q di chuyen tren mpi canh tam giac ^ |,

C6ng cua life dien trirdng khi q di chuyen tren

canh B C cua tam giac:

V = q E B C = 10 ^300.0,l =3.10-^J

C6ng cua life dien tru'dng khi q di chuyen tren canh C A cua tam giac:

= - q E A C = AAB =-1,5.10-^ J

B

B6\g hpc sinh gi6i V$t ly 11, tjp 1 - NguyJn Phu B6ng

AS 1 ^ 1 A E

+ i + + + 1 +

3.31 Mat phang dien tich S tich dien q phan bo deu hai ta'm kirn loai c6 cun|

dien tich S dat 2 ben mat q each mSt q nhffng doan nho l^ Tim hieu die,

tich dien (gia a > 0) Do tinh chat phan bo

dien tich tren mat phang, ta thay mat phang

tich dien chia khong gian lam hai nu'a doi

xi^ng nhau "

V i mat phang v6 han, nen bat ki difdng thang nao vuong goc vdi mat phaiio

cung deu la true doi xuTng cua he dien tich Do do, cac vectd ci/dng do dien

trirdng tai moi diem ben ngoai mat phang deu song song vdi nhau va vu6n»

goc vdi mat phang c6 do Idn bang nhau, hUdng ra xa mat p h i n g neu o > C

(mat phang tich dien du-cfng) va hiTdng ve phia mat phang neu a < 0 (mat

phang tich dien am) NhU" vay cl moi nufa khong gian hai ben mat phang ticli

dien, dien tru'cfng la deu

+ De xac djnh ciTcJng dp dien trUcJng do mat phang tich dien gay ra tai A cad

mat phang mot khoang h, ta chpn mat kin S la mot hinh tru (bieu d i l n bam

difcJng net dut tren hinh ve) c6 diTdng sinh vuong goc vdi mat phang, hai da)

song song (day tren chiJa diem A) each mat phdng mot khoang h va c6 dien del

AS Chpn chieu diTdng ciia phap tuyen n hi/dng ra ngoai mat S V I phdp tuyei

cua mat xung quanh hinh tru vuong goc diTdng siJc nen a = 90° => cosa = f

dien thong qua mat xung quanh bang khong Dien thong toan phan qua mat*

chi con bang dien thong qua hai diy \h c6 gia t n :

N = 2EAS cosa = 2E.AS

+ Dien tich q d ben trong mat AS la dien tich c6 tren phan mat phang c6 die'

tich AS gidi han bdi mat tru: q = a.AS

+ A p dung dinh l i Ostrogradski - Gauss: N = 2E.AS = =>E =

( ^0

+ Dien the do mat ph^ng tich dien q gay ra tai tam k i m loai cdch mat q doan '

Cty TNHH MTV D W H Khann Vi?t

V a v Hieu dien the giffa hai ta'm kim loai la U n = — — — ,

3.32 Hai mat phang rpng v6 han tich dien deu trai dau nhau, mat dp dien mat

±a Chpn go'c dien the d ban tich dien am, true Ox hu'dng vuong goc tij" ban

am sang ban diTdng T i m dien the tai mot diem trong khoang giufa hai ban

B a i g i a i i _ Ap dung ke't qua tim du'pe d bai 10.5 ve

ci/dng dp dien tru'dng do mot mat phang

rpng v6 han tich dien deu gay ra, ta van +<7 dung dinh l i Ostrogradski - Gauss cho he hai mat phang tich dien V i dien tich phan

bo deu tren hai mat phang nen dd dang nhan xet rang ci/dng dp dien triTdng gay bcti

tuTng mat va bdi ca hai mat eo phifdng -a

vuong goc vdi cac mat M a t khac, ciTdng dp dien triTdng c6 dp Idn nhu" nhau tai cac diem

each deu mat phang

Ngoai ra, d trong khoang giffa hai mat phang, veetd E eo chieu tff mat p h i n g

tich dien dffcfng sang mat phang tich dien am Chpn mat kin S la mat tru, c6 hai day song song dien tich AS each deu mat phang va mat xung quanh hinh tru vuong goc vdi matph^ng

+ Dien thong N qua toan bp mat S ehi con bang dien thong qua hai mat day

Doi vdi mat kin S3 thi tdng dai so cac dien tich ben trong mat kin 1^:

Bfll diflng hgc sinh gi6i Vjt ly 11, tjp 1 - Nguygn Phu B6ng cty TNHff Twry-iwyH ggangW"

- Dien the' tai mot diem trong khoang giuTa hai ban: V = Ex = —x

^0

Vay: Dien the tai mot diem trong khoang giiJa hai ban la V = Ex = —x

^0

3.33 Hai ban kim loai phang dat song song each nhau d = lOem duTcIc tieh die^

trai da'u va eung dp Idn Mot thanh dien moi ehieu dai / = 1cm n^m dpc theo

mot diTcJng siJc, hai dau thanh c6 2 dien tich diem eijng dp Idn q = 10

nhi/ng trai da'u Khi quay thanh goc 90° quanh true qua mot diem tren thanli

de thanh vuong goc vdi du'dng siJc, can thiTc hien eong A' = 3.10~'°J Tin\

hieu dien the giiJa 2 ban kim loai

Bai giai '

- TCr ket qua bai 3.32, eu'dng dp dien trUdng giffa hai ban kim loai phing tich

dien trai da'u vdi mat do dien mat ±a la: E = — = 47tka

^0

- Lire dien tac dung vao moi qua cau c6 dp Idn: F = qE = q. 47ika

- Khi quay thanh mot goc 90° quanh mot true qua mot diem baft ki tren thanh

mot goc 90° thi dau kia chuyen dpng dpc theo di/dng siJc so vdi dau nay cua

thanh mot doan s = / nen eong phai thiTc hien la:

A' = Fs = q.47rka/

- Hieu dien the' giiJa hai ban kim loai la: U = Ed

A'd

+ +

Vay: Hieu dien the'gii?a hai ban kim loai la U = 300V + ^

3.34 Mot vat dan tich dien phan bo deu tren be mat vdi mat dp didn mat a

Tinh eu'dng dp dien tru'dng tai mot diem d sat mat ngoai cua vat dan

••iri ;A„!>i f'fe.j ••'ci ii<'.a ri Bai giai

- Dien thong qua mat kin S: N = ^EAS.cosa = ES

- Theo djnh li Ostrogradski - Gauss: N = 88^ - S a d S =

88„

•ES = aS 88, E = 88^ a (trong chan khong 8=1)

Vay: Cufdng dp dien tru'dng tai mot diem sat mat vat dan la E = —

3 35.1^0' ^™ '"^'"'^ ^ ^^^^ '"'^^ P^^" ^^^^ "^^t- ' Tinh dien the tai mot diem each tam qua cau doan r

Bai giai

Xru'dc he't can xac djnh ei/dng dp dien tru'dng gay bdi mat cau kim loai tam

O, ban kinh R, tich dien q > 0

£)jg'm Ai ben ngoai mat cau each tam O mot khoang r > R vf

+ Xet mat eau Si, tam O, ban kinh r chiJa diem Ai Vi li do doi xiJng tai mpi diem tren Si veetd cufdng dp dien tru'dng E deu vuong goc vdi Si (tiJc la

CO phUdng trCing vdi ban kinh), c6 dp Idn h\ng nhau, hU'dng ra xa tam O

neu a > 0, hU'dng ve phia tam O ne'u a < 0

_2i

+ Dien thong qua mat kin Si: N = 47ir E + Theo djnh li Ostrogradski - Gauss:

=> E -47ir^8 kq + Dien the tai Ai: VAI = Er = kq

Diem A2 ben trong mat cau tich dien each

tam O mot khoang r < R: Vi qua cau la vat dang the' nen dien the tai mot diem ben trong qua eau bang dien the tai mot diem tren mat qua cau: r' = R

+ Xet mat cau S2, tam O, ban kinh r = R chiJa diem A'

+ Dien thong qua mat kin S2: N = 4 7t R^E

+ Ap dung djnh li Ostrogradski - Gauss:

^•36 Qu^ cau ban kinh R tich dien deu vdi mat dp dien khoi p Tinh dien the' tai

^iem each tam qua cau mot doan r

69

Boi duSng h o c j i n h gidi vat ly 11, t$p 1 - Nguyin Phu Sfing

B a i giaj

Vi sir phan bo dien tich c6 tinh do'i xiJng cau nen dUcfng svCc dien trifdng ]^

nhffng diTdng thang trting vdi phiTOng ban kinh, hiTdng ra xa tam O cua khCj

cau neu S > 0, hoac hu'dng ve tam O neu S < 0 Hdn niJa, tai cac diem caei,

deu tam O, cUdng do dien tru'dng c6 gia tri nh\i nhau Chon mat kin S la mat

cau dong tam vdi khoi cau va chila diem khao sat

- Diem A], d ben ngoai khoi cau tich dien each tam O mot khoang r > R:

mat cau Sj, tam O, ban kinh r chiJa diem A;: u

+ Dien thong qua mats,: N = E.AS = 471 r^E

+ Theo dinh li Ostrogradski - Gauss:

1 j)jnh nghla: Tu dien la mot he gom hai vat dan dat each dien vdi nhau,

jnSi vat dan du'dc goi la mot ban tu dien Moi tu dien c6 hai ban: ban

diWng va ban am i i | ^ •

2, Dien dung cua tu di^n

Dien dung cua tu dien la dai liTdng dac tru-ng cho kha nang tich dien cua tu

^jgn- C = (Q = IQI = IQ'I la dien tich tu dien; U la hieu dien the giQ-a

hai ban tu) Dien dung cua tu dien phang: C (S la dien tich phan doi dien giffa

47tkd

hai ban t u ; d la khoang each giffa hai ban tu). r ^

Dien dung cua vat dan c6 lap: C = ^ (V la dien the cua vat dan;Q la dien tich ciia vat dan)

eR R Dien dung cua tu dien cau: C = ^—^ (Ri, R2 la ban kinh trong va

ngoai cua tu)

(n 1 )S Dien dung cua tu dien xoay: C = , vcti:

- D i e m A2 d ben trong khoi cau each tam O mot khoang r < R

+ Dien thong ben trong mat cau S2: N = E.AS = E.47t.r'^

+ Theo djnh l i Ostrogradski - Gauss: N = —

V = P ? i ; v a i r < R t h l V = P""' 3E„

3en

47ikd ' " 4 : r k d

3 Ghep cac tu diOn

Ghep song song:

Ghep lien tiep ban am cua tu nay vdi ban dUdng cua tu ke tiep )

II Nang W^ng cua ty di^n

- Nang lirdng cua tu dien: W = - QU = - C U ' = - ^

- Mat do nang liTcJng dien triTdng: Trong khong gian giiJa liai ban tu c6 di6„

trUdng nen c6 the noi nang luTdng cua tu dien la nang lifdng dien tru-dng Goj

V = Sd la the tich viing khong gian giffa hai ban tu thi mat do nang liTdng diet,

- Khi giai cac bai toan ve tinh dien dung, dien tich va hieu dien the" ciia mot tu

dien can chu y:

+ loai tu dien: phang, cau, xoay, ; moi tru'dng giffa hai ban tu dien (s)

+ doi ddn vj hdp phap: ddn vi ciia Q ra (C); dcfn vj cua U ra (V); ddn vj cua

C ra (F)

+ cac diJ kien: noi tu vao nguon: U = const; ngat tu khoi nguon: Q = const

+ dat vao tu mot tam dien moi e'; he gom 2 tu ghep noi tiep: tu 1 (e, di); tu

- Vdi cac bai toan ghep tu can chii y:

+ Khi ghep cac tu chU'a tich dien tru'dc:

• Ghep song song: Ub = U , = U2 = Qb = Qi + Q2 +••.; Cb = C , + C2

I

• Ghep noi tiep: Ub = U i + U 2 + ; Q b = Qi = Q 2 = - - ;

+ Khi ghep cac tu da tich dien triTdc:

• Ghep song song: Ub = U i = U 2 = ; Cb = C i + C 2 +

1 1

+—+

C , C ,

72

• Ghep noi tiep: Ub = U | + U2 + ; 1 1 1 -+ —+

Dinh luat bao toan dien tich cho he c6 lap: SQj = const

Neu mach gom tu dien, nguon dien, dien trd mac vdi nhau thi:

+ Neu trong mach c6 dong dien thi khi giai can: '

• Tinh cU'dng dp dong dien trong cac doan mach

• Tinh hieu dien the' hai dau doan mach chiJa tu dien (bang cac djnh luat

6m)

• Suy ra dien tich tren tiTng tu dien

+ Neu trong mach khong cd dong dien thi khi giai can: ^,

• Viet phUdng trinh dien tich cho tifng doan mach , ,

• Vie't phiTdng trinh dien tich cho cac ban tu noi vdi mot nut mach

• Suy ra hieu dien the, dien tich tren tCrng tu dien. t , |

De xac dinh liTdng dien tich di chuyen qua mot dan mach can:

+ Xac dinh tdng dien tich tren cac ban tu no'i vdi mot dau cua doan mach liic dau: Q

+ Xac djnh tong dien tich tren cdc ban tu no'i vdi dau noi tren cua doan mach luc sau: Q'

+ Suy ra lu'dng dien tich qua doan mach tren: AQ = IQ'-QI V • Can chu y den gidi han hoat dpng cua tu dien khi xac djnh hieu dien the ciTc dai dat vao tu hoac tinh dien triTdng danh thiing cua tu: Ugh = Eghd Vdi bp tu

thUUb),„ = inin{(Ugh)i}

-Nang lu'dng cua bp tu bang tong nang liTdng cua cac tu ghep thanh bp:

Wb= I W i = W, + W 2 +

Trong dien triTdng cua tu dien, cac dien tich thu'dng chuyen dpng theo quy

^ao la dirdng cong nen de giai cac bai toan ve chuyen dpng cua cac dien tich

thu"dng su* dung "PhU(/ngphap toa do" bang each: • • '

73

+ Phan tich chuyen dong cua dien tich thanh hai chuyen dong thanh phan

ddn gian tren hai true toa do Ox, Oy

+ Khao sat chuyen dong rieng re cua dien ti'eh tren hai true toa do do

+ Phoi hdp cac chuyen dong thanh phan thanh chuyen dong thi/c eiia dien tich

Chii y: Cac life thiTdng gap: trong liTc P = mg ; life dien F = qE

- Khi dien tich n^m can b&ng trong dien triTdng cua tu dien ta eung diTa vao

dieu kien can bang da biet de giai quye't cac yeu cau eua bai toan loai nay:

F,+F2+ = 6

C C A C B A I T A P V E T V D I E N

1 D I E N D U N G , D I E N T I C H V A H I E U D I E N T H E CUA T V D I E N

4.1 Tu phang c6 cac ban hinh tron ban kinh 10cm khoang each va hieu dien the

hai ban la 1cm, 108V Giffa 2 ban la khong khi Tim dien tich tu dien

B a i giai

- Dien tich phan doi dien cua hai ban tu la: S = TIR^ = 7t.0,l^ = 0,0l7i (m^)

- Dien dung cua tu dien phang la:

Vay: Dien tich ciia tu dien la Q = 3.10"' C

4.2 Qua cau dien dung C = 50pF tich dien d hieu dien the U = 180V Tinh dien

tich va ban kinh qua cau

B a i giai

- Dien tich cua qua cau: Q = CU = 50.10"'l 180 = 9.10"'C

- Khi qua cau di/dc tich dien Q, dien tich se phan bo deu tren be mat qua clu,

Dien the ciia qua cau la: V = 9 1 0 ^ - ^ = 9 1 0 ^ - ^ ^ ^ ^ = —

sR R R

- Dien dung ciia qua cau la:

C = ^ = > V = ^ = U ^ ^ = 180 R = 0,45m = 4 5 c m

Vay: Dien tich va ban kinh cua qua cau la Q = 9.10"' C va R = 45 cm

4.3 Qua cau dien dung C, = 0,2 j i F tich dien Q = 5.10"^C Noi qua cau n^y vdi

mot qua cau d xa khong tich dien, dien dung C2 = 0,3 n F bang day dan manh

Tinh dien tich moi qua cau sau khi noi

.5.10"^ =3.10"^ C

C 1 + C 2 ^ 0,2 + 0,3

4.4 Tu phing khong khi dien dung C = 2pF di/dc tich dien d hieu dien the U = 600V

a) Tinh dien tich Q cua tu

b) Ngat tu khoi nguon, diTa hai ban tu ra xa de khoang each tang gap 2 Tinh Ci,

Qi, Ui cua tu

c) V i n noi tu vdi nguon, d^a hai ban tu ra xa de khoang each tang gap 2 Ian

TinhC2, Q2, U2cuatu

B a i giai

a) Dien tich Q cua tu ']

Vay: Dien tich cua tu dien la Q = 1,2.10''C. , r

-b) Khi ngat tu khoi nguon: Khi ngat tu khoi nguon thi dien tich khong ddi nen:

V t y : Khi ng^t tu khoi nguon va du^a hai ban tu ra xa gap doi thi dien tich ciia

tu la Qi = 1,2.10''C dien dung cua tu la C, = IpF va hieu dien the cua tu la

U | = 1200 V

Khi van noi tu vdi nguon dien: Khi van noi tu vdi nguon thi hieu dien the

gitta hai ban tu khong doi: U2 = U = 600 V T : ; "

E^ien dung cua tu:C2 =

B6\g hgc sinh gidi Vat ly 11, tap 1 - Nguyin Phu Dfing

Vay: Khi van noi tu vdi nguon dien va du^a hai ban ra xa gap d6i thi dien tic|,

cua tu la Q2 = 0,6.10"'C dien dung cua tu la C2 = IpF va hieu dien thd' cua

la U2 = 600 V

4.5 Mot tu dien cau diTdc ca'u tao bdi mot qua cau ban kinh R, va v6 cau hi^

kinh R2 (Ri < R2) Tinh dien dung ciia tu

Bai giai

Ta c6: Hai ban tu dien la hai mat cau kim loai dong tam ban kinh Ri, R2

- Dien the cua m6i ban:

4.6 Tu phang khong khi, dien tich m6i ban S,

khoang each d noi vdi nguon U ban tren cua

tu diTdc giff CO djnh, ban diTdi c6 be day h,

kho'i lifcJng rieng D dat tren de each dien Bie't

ban tu du'di khong nen len de' Tinh U wwMM/w/Mw^mw/w/,

Bai giai

- Ban tu diTdi khong n6n len de tiJc la trong lu"dng cua ban tu da can bang vdi

lufc dien triTcJng: P = F o mg = qE

vdi E = — 9 — 1^ ciTdng do dien triTdng do mot ban tu gay ra 2ee„S

4 7 Tinh dien dung tiTdng diTcing, dien tich va hieu dien the' trong moi tu trong

' cic tri/dng hdp sau: / '

a) Ba tu ghep song song:

- Dien dung tu'dng diTdng cua bo tu: C = C, + C2 + C3 = 2 + 4 + 6 = 12|iF

- Hieu dien the moi tu: U, = U2 = U3 = U = 100 V

C 3

Hinhd

- Dien tich tu C,: Q, = C,U, = 2.10"' 100 = 2.10^ C

- Dien tich tu C2: Q2 = C2U2 = 4.10 ^100 = 4.10^ C

- Dien tich tu C 3 : Q 3 = C3U3 = 6.10 ^ 100 = 6.10^ C

b) Ba tu ghep noi tie'p:

- Dien dung tiTcfng diTcfng cua botu: — = — + — + —

C Cj C2

= > - = - + — + - = 2 =i>C = 0,5LiF C 1 1,5 3

C2 -L C 3 - L

Hinh a C] C2 C3 Hinhb

.1: u ,

- Hieu dien the cua tuCj: U T = ^ = 2 W2

~ Hieu dien the cua tu C3: U3 = • Hai tu C2, C3 m^c no'i tie'p nhau va mac song song vdi tu Ci:

B6i du3ng hgc sinh gi6i Vjt ly 11, tgp 1 - Nguyen Phij Dgng

- Hieu dien the cua tu C,: U, = U 2 3 = U = 120 V

- Dien tich ciia tu C,: Q, = C U , = 0,25.10"* 120 = 3.10"' C

- Dien tich cua tu C 2 va C.,: Q 2 3 = C23U23 = 0,75.10 ^ 120 = 9 l O ' C

- Dien tich cua tu C 2 : Q 2 = C 2 U 2 = 2.10 ^4 = 0,8.10 ' C

- Dien tich ciia tu C 3 : Q 3 = C3U3 = 10 ^4 = 0,4.10^^ C

4.8 Hai tu khong khi phang Ci = 0,2 |A F, C 2 = 0,4^ F mac song song Bp tu dUdc

tich dien den hieu dien the' U = 450V roi ngat khoi nguon Sau do lap day

khoang giffa 2 ban C 2 bJng dien moi e = 2 Tinh hieu dien the bo tu va d i e n

tich moi tu

Bai giai

- Dien dung cua bo tu trifdc khi ngat khoi nguon:

C = C , + C 2 = 0,2 + 0,4 = 0,6^F

- Dien tich cua bp tu:Q = CU = 0,6.IO-'.450 = 2,7.10^ C

- Dien dung ciia tu C 2 sau khi lap day dien moi:

uieu dien the ciia b6 tu sau khi ngdt khoi nguon: U = = — = 270 V

^ pien tich cua tu C,: Q ; = C , U ; = 0,2.10-^270 = 5,4.10 ^ C

^ p j g n t i c h c u a t u C 2 : Q 2 = C 2 U ^ =0,8.10^^270 = 2,16.10 ^ C Vay: Hieu dien the' bp tu va dien tich moi tu sau khi ngat ra khoi nguon la

U' = 270 V; Q'l =5,4.10-'Cva Q'2 = 2,16.10~'C

4 9 Hai tu khong khi phang c6 Cj = 2 C 2 , mac noi tiep vao nguon U khong doi

Ci/^ng dp dien tru'dng trong Ci thay doi bao nhieu Ian neu nhiing C 2 vao chat

q 2 C 2 2

U ' ^ + Dodo: - ! - = - = l,5

M , E = H^^ = ^ = 1,5

Vay: Cu"cfng dp dien trU'cJng trong Ci t i n g 1,5 Ian

'^•10 Ba ta'm kim loai phing giong nhau dat song song va noi nhiT hinh Dien tich

moi ban S - lOOcn', khoang each giffa hai ban lien tiep d = 0,5cm Noi A, B V(3i nguon U = lOCN

^) Tim dien dung cua C O ty va diSn ti;h tren moi , - 1

tarn kim loai

79

Bfli duOnp hoc sinh gi6i V j t l» 11, t j p 1 - Nguygn Phii D6ng

b) Ng^t A , B khoi nguon Djch chuyen ban b theo

phUdng vuong goc vdi ban mot doan x

Tinh hieu dien the giffa A, B theo x A p dung

a) Dien dung cua bp tu va dien tich tren moi tarn kim loai

- D i e n d u n g c u a b o t u : C = C , + C 2 = 1,77.10-".2 = 3,54.10"" F

~ Hieu dien the moi tu la: U , = U2 = U = 100 V

- D i e n tich cua moi tu: Q, = Q 2 = C i U | = 1,77.10 ".100 = 1,77.10""'C

- Dien tich tren tam kim loai A : Q A = Q i + Q2 = 1,77.10"^2 = 3,54.10"' C

- Dien tich tren tam kim loai B : QB = Q I = Q 2 = 1,77.10^^ C

Vay: Dien dung ciia bp tu la C = 3,54.10 " F; dien tich tren cac ta'm k i m loai

- Hieu dien the cua bp tu:

B a i giai

He thong 4 ban k i m loai tren tu'dng du'dng mach tu nhiT hinh ve:

Dien dung cua t u C b C s :

- Dien dung ti/dng diTdng cua bp tu: C = C12 + C3 = ~Y^~2^ ^°

- Dien tich cua ca bp tu: Q = C U = CoU a) Khi noi A vdi B: K h i noi A, B bang day dan thi c6 sir phan bo lai dien tich nhirhinhve: : ; ) ; ,

Theo djnh luat bao toan dien tich: Q = Q

Vay: Hieu dien the giiifa B va D khi noi A vdi B la U B D = 8 V

Khi lap day giiifa B va D bang dien moi: K h i lap day khoang giffa B, D dien