Electrostatics 01

Q.1 Two identical conducting spheres, having charges of opposite sign, attract each other with a force of 0.108 N when separated by 0.5 m. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of 0.036 N. The initial charges on the spheres are (A) ± 5 ×10 -6 C and _ 15 × 10 -6 C (B) (B) ± 1.0 × 10 -6 C and _ 3.0 × 10 -6 C (C) ± 2.0 × 10 -6 C and _ 6.0 × 10 -6 C (D) ± 0.5 × 10 -6 C and _ 1.5 × 10 -6 C Q.2 Two equal negative charges are fixed at the points [0, a ] and [0,  –a] on the y-axis.  A positive positive charge Q is released released from rest rest at the points [2a, [2a, 0] on the x-axis . The charge charge Q will (A) execute simple harmonic motion about the origin (B) move to the origin and remain at rest (C) move to infinity (D) execute oscillatory but not simple harmonic motion . Q.3 n small drops of same size are charged to V volts each. If they coalesce to form a signal large drop, then its potential will be (A) V/n (B) Vn (C) V n 1/3 (D) V n 2/3 Q.4 Three concentric metallic spherical shell A, B and C or radii a, b and c (a < b < c) have surface charge densities  – , + , and  – respectively. The potential of shell A is : (A)

a + b  – c] (B)  [a  – b + c] (C)  [b  – a  – c] (D) none

Q.5 A solid sphere of radius R is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre? (A) R (B) R/2 (C ( C ) R/3 (D) 2R Q.6 An infinite nonconducting sheet of charge has a surface charge density of 10 C/m2. The separation between two equipotential surfaces near the sheet whose potential differ by 5V is (A) 0.88 cm (B) (B) 0.88 mm (C) 0.88 m (D) 5 × 10 –7 m

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Q.7 Two positively charged particles X and Y are initially far away from each other and at rest. X begins to move towards Y with some initial velocity. The total momentum and energy of the system are p and E. (A) If Y is fixed, both p and E are conserved. (B ) If Y is fixed, E is conserved, but not p. (C) If both are free to move, p is conserved but not E. (D) If both are free, E is conserved, but not p

Q.8 Two particles X and Y, of equal mass and with unequal positive charges, are free to move and are initially far away from each other. With Y at rest, X begins to move towards it with initial velocity u. After a long time, finally

(A ) X will stop, Y will move with velocity u. (B) X and Y will both move with velocities u/2 each. (C) X will stop, Y will move with velocity < u. (D) both will move with velocities < u/2. Q.9 In a uniform electric field, the potential is 10V at the origin of coordinates, and 8V at each of the points(1, 0, 0), (0, 1, 0) and (0, 0, 1). The potential at the point (1, 1, 1) will be (A) 0 (B ) 4 V (C) 8 V (D) 10 V Q.10 In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges are placed at (n  – 1) corners. At the centre, the intensity is E and the potential is V. The ratio V/E has magnitude. (A) r n (B ) r (n  – 1) (C) (n  – 1)/r (D) r(n  – 1)/n Q.11 The equation of an equipotential line in an electric field is y = 2x, then the electric field strength vector at (1, 2) may be (A) 4i 3j (B) 4 i 8j (C) 8 i 4 j (D) -8i 4j Q.12 A charge 3 coulomb experiences a force 3000 N when placed in a uniform electric field. The potential difference between two points separated by a distance of 1 cm along the field lines is (A) 10 V (B) 90 V (C) 1000 V (D) 9000V Q.13 In a certain region of space, the potential is given by : V = k[2x 2 – y2 + z2]. The electric field at the point (1, 1, 1) has magnitude = (A) k 61/2 (B) 2k 61/2 (C) 2k 3 1/2 (D) 4k 3 1/2 Q.14 Uniform electric field of magnitude 100 V/m in space is directed along the line y = 3 + x. Find the potential difference between point A (3, 1) & B (1, 3) (A) 100 V (B) 200 2 1/2 V (C) 200 V (D) 0 Q.15 Point P lies on the axis of a dipole. If the dipole is rotated by 90° anticlock wise, the electric field vector E at P will rotate by (A) 90° clock wise (B) 180° clock wise (C) 90° anti clock wise (D) none Q.16 A positive charge q is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance l . Force on charge q is : (A ) in the direction parallel to vector  l  (B) in radial direction (C) in a direction which depends on the magnitude of charge density in sphere (D) direction can not be determined

Q.17 Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1,2), (2,4) and (4,1) show electrostatic attraction while pairs (2,3) and (4,5) show repulsion. Therefore ball 1 must be (A) positively charged (B) negatively charged (C) neutral (D) made of metal Q.18 Four charges of 1 C, 2 C, 3 C, and  – 6C are placed one at each corner of the square of side 1m. The square lies in the x-y plane with its centre at the origin. (A ) The electric potential is zero at the origin. (B) The electric potential is zero everywhere along the x-axis only of the sides of the square are parallel to x and y axis. (C ) The electric potential is zero everywhere along the z-axis for any orientation of the square in the xy plane. (D) The electric potential is not zero along the z-axis except at the origin. Q.19 Select the correct statement : (Only force on a particle is due to electric field) (A) A charged particle always moves along the electric line of force. (B) A charged particle may move along the line of force (C) A charge particle never moves along the line of force (D) A charged particle moves along the line of force only if released from rest. Q.20 A conducting sphere of radius r has a charge. Then (A) The charge is uniformly distributed over its surface, if there is an external electric field. (B) Distribution of charge over its surface will be non uniform if no external electric field exist in space. (C) Electric field strength inside the sphere will be equal to zero only when no external electric field exists (D) Potential at every point of the sphere must be same Q.21 For a spherical shell (A) If potential inside it is zero then it necessarily electrically neutral (B) electric field in a charged conducting spherical shell can be zero only when the charge is uniformly distributed. (C) electric potential due to induced charges at a point inside it will always be zero (D) none of these Q.22 A proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles ? (A) They have different speeds (B ) They have same momentum (C) They have same kinetic energy (D) They have been subjected to same force