Unit 1c kho tài liệu bách khoa

VERY SHORT-AND SHORT-ANSWERS QUESTIONS 81 A body has a negative charge of 1.6 C Calculate the number of excess electrons on it 82 (a) Write Coulomb’s law in vector form (b) Find the electric field intensity at a point at a distance r from a charge of q coulomb in space (AISCE Delhi 1994) 83 Write an expression for the work done in deflecting an electric dipole in a uniform electric field through an angle θ from the equilibrium position 14 84 Calculate the charge on the nuclide N 85 Write an expression for the capacitance of a parallel plate capacitor having a dielectric slab between the plates 86 Calculate the electric field between two metal plates mm apart connected to a V battery (AISSCE Delhi 1993) 87 A point charge of 8.86 C is placed at the centre 20 µ F of a cube of side 10 cm Calculate the flux passing through its one face 88 Calculate the capacitance of the capacitor C in C 20 µ F Fig 1.3 The equivalent capacitance of the system between the points A & B is 30 µ F (AISSCE 1995) 89 What is the area of the plates of a parallel plate capacitor of capacitance F and with separation between the plates 0.5 cm? (AISSCE Delhi 1990C) A S Chand & Company Limited B 20 µ F 90 A 900 pF capacitor is charged by a 100 V battery How much electrostatic energy is stored by the capacitor? (AISSCE Delhi 1990) 91 How does the potential V due to short electric dipole on its axis vary with distance r from the centre of the dipole? 92 What is the value of dielectric constant for a perfect conductor? 93 Does the work done in moving a charge in an electric field from one point to another depend on the path followed by it? 94 Is the electric flux a scalar quantity ? 95 A conductor A with a cavity is given a charge Q Another conducting body B having charge + q is inserted into the cavity, keeping it insulated from A What will be the total chrage on the outside surface of A ? See Fig 1.4 +q B 96 Are there points around an electric dipole where the field due to it is not zero but the potential is zero ? A 97 What is the nature of the electric field between the plates of a parallel plate capacitor ? 98 What happens when the plates of a charged capacitor are connected by a metallic wire ? 99 Two insulated conductors having capacitances C1 and Fig 1.4 C2 are given charges Q1 and Q2 respectively The two conductors are then connected by a thin wire What is the ratio of the new charges on the conductors after redistribution ? 100 Can the electric potential be zero at a point where the electric field is not zero ? 101 An isolated metallic conductor is positively charged Does its mass increase, decrease or remain the same ? 102 What is the relation between the absolute permittivity and the relative permittivity of a medium ? S Chand & Company Limited 103 What is the direction of the electric field at a point on the equatorial line of an electric dipole ? 104 How much work is done in deflecting an electric dipole of dipole moment p in a uniform electric field E through 180° from the equilibrium position 105 A proton and an electron are free to move in an electric field Which one will have greater acceleration and why ? 106 What is the work done by the electric field of the nucleus of an atom of atomic number Z on an orbital electron when it completes one revolution in an orbit of radius r 107 The electric field is discontinuous across the surface of a charged conductor Is electric potential also discontinuous there ? 108 How is the electric field at a point related to the potential at that point ? 109 What is the direction of the electric field at any point on an equipotential surface ? 110 Write two uses of a capacitor (AISSCE 1994) 111 How is dielectric constant expressed in terms of capacitance ? (AISSCE Delhi 1992 C) 112 In a parallel plate capacitor, the capacitance increases from 4µF to 80µF on introducing a dielectric medium between the plates What is the dielectric constant of the medium ? (AISSCE 1996) 113 What is the work done in moving a charge of 10 nC between two points on an equipotential surface (AISSCE Delhi 1996) 114 Force between two point electric charges kept at a distance d apart in air is F If the charges are kept at the same distance in water, how does the force between them change ? (AISSCE Delhi 1997) 115 Two point electric charges of unknown magnitude and sign are placed a distance apart The electric field intensity is zero at a point not between the charges but on the line joining them Write two essential conditions for this to happen (AISSCE Delhi 1997) 116 Sketch the electric lines of force for two positive charges Q1 and Q2 (Q1 > Q2) separated by a distance d (AISSCE Delhi 1997 C) S Chand & Company Limited 117 Sketch two equipotential surface for a point charge (AISSCE 1997 C) 118 In a medium the force of attraction between two point charges, distance d apart, is F What distance apart should these be kept in the same medium so that the force between them becomes (i) F (ii) F/3 ? (AISSCE 1998) 119 Draw equipotential surface in a uniform electric field How does the force between the two point charges change if the dielectric constant of the medium in which they are kept increases ? (AISSCE 1999) 120 Draw an equipotential surface in a uniform electric field (AISSCE Delhi 2000) 121 What is the amount of work in moving a 100 nC charge between two points cm apart on an equipotential surface ? (AISSCE 2000) ANSWERS 81 Number of excess electrons Q 1.6 n= e = = 1019 −19 1.6 × 10 ""# 82 (a) F12 = k (b) E = kq r q1 q r2 ""# r! 12 , F21 where k = =k q1 q r2 r! 21 4π ε 83 W = PE (1 – cos θ) 84 14 7N contains protons Therefore, S Chand & Company Limited Q = 7e = × 1.6 × 10–19C = 1.12 × 10–18 C 85 E = q 4π ε0 x2 where A is the area of each plate, d is the distance between the plates, t is the thickness of the dielectric slab, and K is the dielectric constant of the slab 86 E = V/d = × 10 −1 −3 = 6.7 × 10 Vm 87 From Gauss’s theorem, flux through the cube, φ = = 8.86 8.85 × 10 Flux through each face = 12 −12 = 10 q ε0 Nm / C 11 ( φ ) = 1.67 × 10 Nm /C 88 All the three capacitors of 20 µF are in parallel between the points C & B, so their equivalent capacitance is 60 µF Now for the series combination between A & B, we have 60 + S Chand & Company Limited C = 30 or 1 1 = − = C 30 60 60 C = 60 µF or 89 Capacitance of a parallel plate capacitor, C = Here C=2F d = cm = 0.5 × 10–2 m So A= = d Cd ε0 × 0.5 × 10 8.86 × 10 −2 −12 = 1.1 × 10 m 90 Energy stored in Capacitor U = = ε0 A CV 2 −12 × 900 × 10 × (100) = 4.50 × 10–6 J 91 V∝ r2 92 For a perfect conductor, K = ∞ 93 No 94 Yes It is the scalar product of → E and → A S Chand & Company Limited 95 The charge + q inside the cavity will induce a charge –q on the inner surface of conductor A and hence + q on the outer surface of A So the total charge on the outside surface of A will be (Q + q) 96 All the points on the equatorial line have this property 97 It is uniform 98 The charge flows through the wire and the energy stored in the capacitor is dessipated in the form of heat energy 99 C1 / C2 100 Yes 101 When a conductor is positively charged, some electrons are removed from it So the mass of the conductor decreases 102 Relative permittivity = Absolute permittivity Permittivity of free space 103 It is opposite to the direction of the electric dipole moment vector 104 Work done W = pE (1– cos θ) Here θ = 180° Therefore W = pE 105 The force acting on a charge q in an electric field E is: F = qE Acceleration a = qE m Thus a ∝ m Since acceleration produced is inversely proportional to the mass of the particle, the acceleration of the electron will be greater S Chand & Company Limited 106 Zero 107 No, the potential is continuous 108 Electric field at a point is the negative of the potential gradient at that point: E = – ∇V  ∂ = −i  ∂x + j ∂ ∂y +k  V ∂z  ∂ Thus the x, y and z components of the field are Ex = − ∂V ∂x , Ey = − ∂V ∂y , Ez = − ∂V ∂z 109 The electric field at any point on an equipotential surface is normal to the surface 110 Capacitors are used (i) to store charge and electrical energy, and (ii) to establish electric fields of required pattern 111 Dielectric constant K = C′ , where C is the capacitance of a capacitor with vacuum between the C plates and C ′ is the capacitance of the same capacitor when the space between the plates is filled with the dielectric 112 Dielectric Constant K = C′ C = 80 µF = 20 µF S Chand & Company Limited 113 Zero 114 Since the dielectric constant of water is 80, the force between the charges in water becomes F/ 80 115 The two charges are of (i) unequal magnitudes, and (ii) opposite in sign 116 Q2 Q1 Fig 1.14 117 Equipotential surface Fig 1.15 S Chand & Company Limited 118 Force between the two charges depends on the distance between them as F ∝ d2 (i) For the force to become F, The distance must be d / (ii) For the force to become F/3 the distance must be d 119 Equipotential surface Fig.1.16 Force F ∝ , where K is the dielectric constant of the medium Thus force decreases with K increase of dielectric constant S Chand & Company Limited 120 Same as Q 119 121 Zero There is no change of potential on an equipotential surface Hence no work is done in moving a charge on it S Chand & Company Limited