General physics 2 electricity magnetism lecture 1

Ngac An Bang, Faculty of Physics, HUS GENERAL PHYSICS Electricity & Magnetism Physics Ngac An Bang, Faculty of Physics, HUS  Text book: Fundamentals of Physics, David Halliday et al., 8th Edition Physics for Scientists and Engineers, Raymond A Serway and John W Jewett, 6th Edition  Instructor: Dr Ngac An Bang Faculty of Physics, Hanoi University of Science ngacanbang@hus.edu.vn  Homework: will be assigned and may be collected  Quizzes and Exams:  There will be at least two (02) 15-minute quizzes  There will be a mid-term exam and a final exam  Grading policy:  Homework and Quizzes: 20 %  Midterm exam: 20 %  Final exam: 60 % Physics Ngac An Bang, Faculty of Physics, HUS Lecture Electric Charge and Field  Electric Charges  Coulomb’s Law  Electric Fields  Electric Field of a Continuous Charge Distribution  Motion of Charged Particles in a Uniform Electric Field Electric Charge and Field Ngac An Bang, Faculty of Physics, HUS Mother and daughter are both enjoying the effects of electrically charging their bodies Each individual hair on their heads becomes charged and exerts a repulsive force on the other hairs, resulting in the “stand-up’’ hairdos that you see here (Courtesy of Resonance Research Corporation) Electric Charge and Field Electric Charge Electric charge Ngac An Bang, Faculty of Physics, HUS Some simple experiments demonstrate the existence of electric forces and charges  There are two types of charge Convention dictates sign of charge:  Positive charge  Negative charge  Like charges repel, and opposite charges attract Electric Charge and Field Electric Charge Ngac An Bang, Faculty of Physics, HUS Quantization of Charge Charge is quantised  The smallest unit of “free” charge known in nature is the charge of an electron or proton, which has a magnitude of e = 1.602 x 10-19 C  Charge of any ordinary matter is quantized in integral multiples of the elementary charge e, Q = ± Ne  An electron carries one unit of negative charge, -e,  While a proton carries one unit of positive charge, +e  Note that although quarks (u, d, c, s, t, b) have smaller charge in comparison to electron or proton, they are not free particles Electric Charge and Field Electric Charge Charge conservation Ngac An Bang, Faculty of Physics, HUS A universal conservation law • In a closed system, the total amount of charge is conserved since charge can neither be created nor destroyed • A charge can, however, be transferred from one body to another • The β- reaction n → p + e + νe 0e = 1e -1e + 0e n(udd), p(uud) d → u + e + νe • Electron-positron annihilation e- + e+ → γ + γ • Pair production (γ-conversion) γ → e- + e+ Electric Charge and Field Electric Charge Ngac An Bang, Faculty of Physics, HUS Some basic concepts  All materials acquire an electric charge  Neutral object: Total positive charge Q+= Total negative charge Q-  Positively charged object: Q+ > Q-,  Negatively charged object: Q+ < Q In this part, we consider only two types of materials • Conductors: Electrical conductors are materials in which some of the electrons are free electrons that are not bound to atoms and can move relatively freely through the material; • Insulators: are materials in which electrons are bound to atoms and can not move freely through the material Electric Charge and Field Charge Manipulation Ngac An Bang, Faculty of Physics, HUS Charge transfer by contact Charging Objects By Induction Electric Charge and Field Coulomb’s Law Ngac An Bang, Faculty of Physics, HUS Coulomb’s Law Consider a system of two point charges, q1 and q2, separated by a distance r in vacuum  The force F12 exerted by q1 on q2 is given by Coulomb's law   q1q  q1q r F12  k r  k r r r  The force F21 exerted by q2 on q1 is given by   F21   F12  The Coulomb constant k in SI units has the value Nm k  9875  10 4 C2  The constant ε0 is known as the permittivity of free space and has the value   8.854  10 -12 C2 Nm 10 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Superposition principle Continuous charge distribution • Charge distribution Q    qi  Q   dq i V • Electric field at P due to Δq      q i ri dq r Ei   d E  4 ri ri 4 r r • Superposition     E   Ei  E   dE i 24 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field of a Rod A non-conducting rod of length l with a uniform positive charge density λ and a total charge q is lying along the x-axis, as illustrated in figure Calculate the electric field at a point P(x0,0) located along the axis of the rod Calculate the electric field at a point Q(0,y0) located along its perpendicular bisector 25 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field of a Rod A non-conducting rod of length l with a uniform positive charge density λ and a total charge q is lying along the x-axis, as illustrated in figure Calculate the electric field at a point P(x0,0) located along the axis of the rod dq   dx  dE   dq i 4 ( x  x ) l /  dx  i  4  l / ( x  x )    l q E i  i 2 2 4 ( x  l ) 4 ( x  l )   E   dE  x  l  q  E i 4 x Point charge 26 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field of a Rod A non-conducting rod of length l with a uniform positive charge density λ and a total charge q is lying along the x-axis, as illustrated in figure Calculate the electric field at a point Q(0,y0) located along its perpendicular bisector      dx sin  i  cos  j 2 4 ( y  x )     dx dE '   sin  i  cos  j 2 4 ( y  x )      E   dE   ( dE x  dE y )   dE y  dE      E   d E y   dE cos  j   4  dx cos    ( y 02  x ) j 27 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field of a Rod  E  4 dx cos    ( y 02  x ) j y d x  y tan   dx  cos  2 2 x  y  y (1  tan  )      y max cos  d   E j sin  max j 2  4  max y (1  tan  ) cos  4 y     l/2 l E j j 2 2 4 y 4 y y  l y0  l  E q 4 y y 02  l  j y  l Point charge  q  28 E j 4 y 02 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field of a Circular Arc 29 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field on the Axis of a Ring A non-conducting ring of radius R with a uniform charge density λ and a total charge Q is lying in the xy-plane, as shown in figure Compute the electric field at a point P, located at a distance z from the center of the ring along its axis of symmetry  Let’s consider a small length element dl on the ring The amount of charge contained within this element is dq = λdl  The electric field dE created by the charge dq at point P is   dE  dq r 4 r r    dE  dE z  dE  dE  dq 4 R  z   30 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field on the Axis of a Ring  Using the symmetry argument illustrated in this figure, we see that the electric field at P must point in the z+ direction      E   dE   dE z   dE    dE z  Upon integrating over the entire ring, we obtain    E   d E z   dE cos  n   dq z E  n 2 2 1/ 4 ( R  z ) ( R  z ) ring   z E dl n 2 3/  4 ( R  z ) ring  E  Qz n 2 3/ 4 ( R  z ) 31 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field on the Axis of a Ring  The electric field at point P a distance z from the center of the ring along its axis  E  Qz n 2 3/ 4 ( R  z ) • At the center O: z = 0, E = • In the limit z >> R : Q  n Point charge 4 z  Graphical representation Q E0  4 R E (z) z/R  3/ 2 E0 z / R     E(z)/E  E (z)  0.4 0.2 -10 -8 -6 -4 -2 0.0 z/R -0.2 -0.4 32 10 Electric Charge and Field Electric Field of a Continuous Charge Distribution Ngac An Bang, Faculty of Physics, HUS Electric Field due to a Charged Disk A circular plastic disk of radius R that has a positive surface charge of uniform density σ on its upper surface is shown in the figure on the right What is the electric field at point P, a distance z from the disk along its central axis?    ˆ z E 1  k 2  z R  33 Electric Charge and Field Motion of Charged Particles in an Electric Field Ngac An Bang, Faculty of Physics, HUS A point charge in an electric field  A particle of charge q and mass m is placed in an electric field E, the electric   force exerted on the charge is F  qE  If this is the only force exerted on the particle, it must be the net force and causes the particle to accelerate according to Newton’s second law    F  qE  m a  If the particle has a positive charge, its acceleration is in the direction of the electric field  If the particle has a negative charge, its acceleration is in the direction opposite the electric field 34 Electric Charge and Field Motion of Charged Particles in an Electric Field Ngac An Bang, Faculty of Physics, HUS A point charge in a uniform electric field An electron enters the region of a uniform electric field as shown in the figure below, with initial velocity vi = 3.00 x106 m/s and E = 200 N/C The horizontal length of the plates is l = 0.100 m A Find the acceleration of the electron while it is in the electric field B If the electron enters the field at time t = 0, find the time at which it leaves the field C If the vertical position of the electron as it enters the field is yi = 0, what is its vertical position when it leaves the field 35 Electric Charge and Field Motion of Charged Particles in an Electric Field Ngac An Bang, Faculty of Physics, HUS A point charge in an electric field A negatively charged particle -q is placed at the center of a uniformly charged ring, where the ring has a total positive charge Q The particle, confined to move along the z axis, is displaced a small distance z along the axis (where z