Physics-1. ELECTROSTATICS

1. ELECTROSTATICS SECTION – I : STRAIGHT OBJECTIVE TYPE 14.1 A point charge + Q is placed at the centroid of an equilateral triangle. When a second charge + Q is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge is 8 N. The magnitude of the net force on the central charge when a third charge + Q is placed at another vertex of the triangle is : (A) zero (B) 4 N (C) 4 N (D) 8 N 14.2 The electric field inside a sphere which carries a charge density proportional to the distance from the origin  =  r (  is a constant) is : (A) r3 40 (B) r2 40 (C) r2 30 (D) none of these 14.3 A particle of charge – q & mass m moves in a circle of radius r around an infinitely long line charge on linear charge density +  . Then time period will be. (A) T = 2 r (C) T = 1 (B) T2 = (D) T = 4 2 m r 2k q –q where k = 4 0 14.4 An infinite long plate has surface charge density  , As shown in the fig. a point charge q is moved from A to B. Net work done by electric field is : (A)  q 20  q (X1 – X2) (B)  q 20  q  (X2 – X1) (C) 0 (X2 – X1) (D) 0 ( 2 r r ) 14.5 Figure Shows two large cylindrical shells having uniform linear charge densities +  and –  . Radius of inner cylinder is 'a' and that of outer cylinder is 'b'. A charged particle of mass m, charge q revolves in a circle of radius r. Then its speed 'v' is : (Neglect gravity and assume the radii of both the cylinders to be very small in comparison to their length.) (A) (B) + (C) (D) 14.6 Figure shows three circular arcs, each of radius R and total charge as indicated. +Q The net elecric potential at the centre of curvature is : Q Q 2Q Q –2Q (A) 2 0 R (B) 4 0 R (C) 0 R (D) 0 R 14.7 An electric field is given by Ex = – 2x kN/C. The potential of the point (1, –2), if potential of the point (2, 3 4) is taken as zero, is (A) – 7.5 x 103 V (B) 7.5 x 103 V (C) – 15 x 103 V (D) 15 x 103 V 14.8 Two concentric uniformly charged spheres of radius 10 cm & 20 cm are arranged as shown in the figure. Potential difference between the spheres is : (A) 4.5 x 1011 V (B) 2.7 x 1011 V (C) 0 (D) none of these 14.9 Figure shows an electric line of force which curves along a circular arc. The magnitude E of electric field intensity is same at all points on this curve and is equal to E. If the A B potential at A is V, then the potential at B is :  R   (A) V – ER  (B) V – E2R sin 2 (C) V + ER  (D) V + 2ER sin 2 14.10 Figure shows a solid hemisphere with a charge of 5 nC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15 cm. The electric potential at point P due to the hemisphere, is : (A) 150 V (B) 300 V (C) 450 V (D) 600 V 14.11 A point charge Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R. The potential of the sphere is (d > R) : (A) 1 4 0 , Q (d– R) (B) 1 , Q 4 0 d (C) 1 , Q 4 0 R (D) zero 14.12 Two point dipoles p kˆ & p kˆ 2 are located at (0, 0, 0) & (1m, 0, 2m) respectively. The resultant electric field due to two dipoles at the point (1 m, 0, 0) is : (A) 9p kˆ 32 0 (B) – 7p kˆ 32 0 (C) 7p kˆ 32 0 (D) none of these 14.13 A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant torce on the ring due to dipole is : kPQ (A) zero (B) 2kPQ R3 kPQ (C) R3 (D) R3 only if the charge is uniformly distributed on the ring. 14.14 A charge Q is placed at a distance of 4R above the centre of a disc of radius R. The 4R magnitude of flux through the disc is  . Now a hemispherical shell of radius R is placed over the disc such that it forms a closed surface. The flux through the curved surface taking direction of area vector along outward normal as positive, is (A) zero (B)  (C) –  (D) 2  14.15 A conducting disc of radius R rotates about its axis with an angular velocity  . Then the potential difference between the centre of the disc and its edge is (no magnetic field is present) : (A) zero (B) me2R2 2e (C) u meR3 3e (D) emeR2 2 14.16 At distance 'r' from a point charge, the ratio v2 represented by : (where 'u' is energy density and 'v' is potential) is best (A) (B 14.17 A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and having uniformly distributed positive charge. A ring of radius r(< 0 carries uniform linear charge density –  C/m. y' 14.55 Then the electric potential (in volts) at point P whose coordinates are ( 0m,  R m ) is 2 1  1  (A) 4 0 2 (B) 0 (C) 4 0 4 (D) cannot be determined 14.56 Then the direction of electric field at point P whose coordinates are ( 0m,  R m ) is 2 (A) Along positive x-direction (B) Along negative x-direction (C) Along negative y-direction (D) None of these 14.57 Then the dipole moment of the ring in C–m is (A) – 2R2ˆi (B) 2R2ˆi (C) – 4R2ˆi (D) 4R2ˆi SECTION – V : MATRIX - MATCH TYPE 14.58 In each situation of column-I, some charge distributions are given with all details explained. In column- II. The electrostatic potential energy and its nature is given situation in column-II. Then match situation in column-I with the corresponding results in column-II. Column - I Column - II –Q 1 Q2 (A) A thin shell of radius a and having (P) a charge – Q uniformly distributed over its surface as shown 8 0 a in magnitude 5a 1 Q2 (B) A thin shell of radius 2 and having –Q (q) 20 0 a in magnitude a charge – Q uniformly distributed over its surface and a point charge – Q placed at its centre as shown. –Q 1 Q2 (C) A solid sphere of radius a and having (r) a charge – Q uniformly distributed throughout its volume as shown. 5 0 a in magnitude (D) A solid sphere of radius a and having –Q a charge – Q uniformly distributed (s) Positive in sign throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge – Q as shown 14.59 Column I gives certain situations involving two thin conducting shells connected by a conducting wire via a key K. In all situations one sphere has net charge +q and other sphere has no net charge. After the key K is pressed, column II gives some resulting effect. Match the figures in Column I with statements in Column II. (A) (B) +q K shell I +q K shell I initially no net charge shell II initially no net charge shell II (p) charge flows through connecting wire (q) Potential energy of system of spheres decreases. initially no net charge (C) (r) No heat is produced. shell II +q (D) shell II (s) The sphere I has no charge after equilibrium is reached. (t) charge does not flows through connecting wire SECTION – VI : SUBJECTIVE ANSWER TYPE SHORT SUBJECTIVE 14.60 A positive charge + Q is fixed at apoint A. Another positively charged particle of mass m and charge + q is projected rom a point B with velocity u as shown in the figure. The point B is at large distance from A and at distance 'd' from the line AC. The initial velocity is parallel to the line AC. The point C is at very large distance from A. Find the minimum distance (in meter) of + q from + Q during the motion. Take Qq = 4 0 mu2d and d = ( 2 –1) meter. 14.61 Consider a cube of side a = 0.1 m placed such that its six faces are given by equations x = 0, x = +a, y = 0, y = +a, z = 0 and z = +a, plaeced in electric field given by → = x2ˆi  yˆj N/C. Find the electric flux crossing out of the cube in the unit of 10–4 N m2/C. LONG SUBJECTIVE 14.62 A charged particle is in equilibrium at a height h from a horizontal infinite line charge with uniform linear charge density. The charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically). Prove that the motion of the charged particle will be simple harmonic and find its time period. 14.63 Two point charges are placed at point a and b. The field strength to the right of the E x charge Qb on the line that passes through the two charges varies according to a law that is represented graphically in the figure. Find the signs of the charges & ratio of Q magnitudes of charges a Qb and the distance X2 of the point from b where the field is maximum, in terms of 𝑙 & x1. The electric field is taken positive if its direction is towards right and negative if its direction is towards left. 14.64 In the figure shown a conducting sphere of inner radius 'a' and outer radius 'b' is given a charge Q. A point charge 'q' is placed in the cavity of this sphere at distance 'x' ( b. Also find the electric potential at point C. C q r b P a 14.65 A solid sphere of radius 'R' has a cavity of radius R 2 . The solid part has a uniform charge density '  ' and cavity has no charge. Find the electric potential at point 'A'. Also find the electric field (only magnitude) at point 'C' inside the cavity.