Title 17. Electrostatics Hard.pdf ✅

1. Two point charges q and –q are at positions (0, 0, d) and (0, 0, –d) respectively. What is the electric field at (a, 0, 0) ? (a) k ˆ 4 (d a ) 2qd 2 2 3/ 2  0 + (b) k ˆ 4 (d a ) qd 2 2 3/ 2  0 + (c) k ˆ 4 (d a ) 2qd 2 2 3/ 2  0 + − (d) k ˆ 4 (d a ) qd 2 2 3/ 2  0 + − 2. Two particles having positive charges + Q and + 2Q are fixed at equal distance x from centre of an conducting sphere having zero net charge and radius r as shown. Initially the switch S is open. After the switch S is closed, the net charge flowing out of sphere is - + Q x r x +2Q S (a) x Qr (b) x 2Qr (c) x 3Qr (d) x 6Qr 3. Figure shows three circular arcs, each of radius R and total charge as indicated. The net electric potential at the centre of curvature is- 45o 30o R +3Q –2Q Q (a) 2 R Q  0 (b) 4 R Q  0 (c) R 2Q  0 (d) R Q  0 4. Let r R Q P r 4 ( )  = be the charge density distribution for a solid sphere of radius R and total charge Q. For a point ‘p’ inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is – (a) 0 (b) 2 0 1 4 r Q   (c) 4 0 2 1 4 R Q r   (d) 4 0 2 1 3 R Q r   5. Two points P and Q are maintained at the potentials of 10V and –4V, respectively. The work done in moving 100 electrons from P to Q is. (a) – 9.60 × 10–17 J (b) 9.60 × 10–17 J (c) – 2.24 × 10–16 J (d) 2.24 × 10–17 J 6. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/ q equals – (a) − 2 2 (b) – 1 (c) 1 (d) 2 1 − 7. An isolated and charged spherical soap bubble has a radius 'r' and the pressure inside is atmospheric. If 'T' is the surface tension of soap solution, then charge on drop is - (a) 0 2rT 2  (b) 8  r 0 2rT (c) 8  r 0 rT  (d) 8  r 0 2rT  8. Calculate the net force acting on the charge present at the origin - q –q(a,a) q1 q 45o (a) 2 a kqq 2 1  (b) 2 1 2a kqq + 2 1 2a kqq (c)       − 2 1 2 a kqq 2 1 (d)       − 2 2 1 a kqq 2 1 9. Calculate the net force acting on q0 - q q a q0 a a a a a a q q q (a) 2 0 2a kqq (b) 2 0 (a / 2) kqq (c) Zero (d) 2 0 a kqq 10. The position of the point where net electric field will be zero - 4Q –Q a (a) (1+ a) m from 4Q (b) a/2 m from – Q (c) 1m from 4Q (d) Neutral point not posible 11. Four point positive charges of same magnitude(Q) are placed at the corners of a square. Find the electric field at the centre of the square–
Q Q Q Q (a) 2 a 4kQ (b) 2 (a / 2) 4kQ (c) 0 (d) 2 ( 2a) 4kq 12. A charge –q is placed at (0, 0, – z) where z << a. On releasing –q from this position– Q Q Q Q a a y x a a (a) – q will move towards z = –  (b) – q will move towards z =  (c) – q will move to and fro about the origin (d) – q will remain stationary at (0, 0, – z) 13. Two identical charges of value Q each are placed at (–a, 0) and (a, 0). The co-ordinates of the points where net electric field is zero and maximum are respectively- (a) (0, 0), (0, 0) (b) (0, a/ 2 ), (0, 0) (c) (0, 0), (0, a/ 2 ) (d) (a/ 2 , 0), (0, a/ 2 ) 14. Which of the following diagram is correct? (a)  + + + Negatively charge rod – – –  Neutral metallic plate (b)  + + + Negatively charge rod – – –  Neutral metallic plate + + + + + + (c) External electric field  Neutral metallic plate E   e – e – e – (d) Neutral plate External field – – – + + + 15. In the adjoining figure the electric field lines for charges q1 and q2 are shown. Identify the sign of the charges- q1 q2 (a) Both negative (b) Upper charge is negative and lower is positive (c) Both positive (d) Upperchargeis positive and lower is negative 16. Two particles of masses m and 2m and charges 2q and 2q are placed in a uniform electric field E and allowed to move for the same time. The ratio of kinetic energies will be - (a) 2 : 1 (b) 8 : 1 (c) 4 : 1 (d) 1 : 4 17. Find the net force on –2q - a a a q –2q q (a) 2 2 a 3kq (b) 2 2 a 2 3kq (c) Zero (d) None 18. If an object has a net charge of –1 coulomb, the number of excess electrons it possesses is- (a) 1.6 × 10–19 (b) 6.25 × 1018 (c) 6.25 × 1020 (d) 6.25 × 1017 19. Two metallic spheres of same mass are given equal and opposite charges; then- (a) The mass of positively charged sphere increases (b) The mass of both spheres remains the same (c) The mass of negatively charged sphere increases (d) The mass of both spheres increases 20. Two small identical spheres having charges + 10μC and –90μC attract each other with a force of F newton. If they are kept in contact and then separated by the same distance, the new force between them is- (a) F/6 (b) 16F (c) 16F/9 (d) 9F
21. If two like charges of magnitude 1 × 10–9 coulomb and 9 ×10– 9 coulomb are separated by a distance of 1 meter, then the point on the line joining the charges, where the force experienced by a charge placed at that point is zero, is- (a) 0.25 m from the charge 1 × 10–9 coul (b) 0.75 m from the charge 9 × 10–9 coul (c) Both A and B (d) At all points on the line joining the charges 22. Four equal charges, each +q are placed on the four corners of a square of side a. Then the coulomb force experienced by one charge due to the rest of three is -          = 4 0 1 K (a) 2 2 (2 2 +1)Kq / 2a (b) 3Kq2 /a2 (c) 2 2 Kq2 /a2 (d) Zero 23. Two balls with equal charges are in a vessel with ice at –100C at a distance of 25 cm from each other. On forming water at 0 0C, the balls are brought nearer to 5 cm for the interaction between them to be same. If the dielectric constant of water at 0 0C is 80, the dielectric constant of ice at –100C is- (a) 40 (b) 3.2 (c) 20 (d) 6.4 24. Two unlike charges of the same magnitude Q are placed at a distance d. The intensity of the electric field at the middle point in the line joining the two charge is - (a) Zero (b) 2 4 0d 8Q  (c) 2 4 0d 6Q  (d) 2 4 0d 4Q  25. In nature, the electric charge of any system is always equal to - (a) Half integral multiple of the least amount of charge (b) Zero (c) Square of the least amount of charge (d) Integral multiple of the least amount of charge 26. Charge Q, is divided into two parts which are then kept some distance apart. The force between them will be maximum if the two parts are having the charge- (a) Q/2 each (b) Q/4 and 3Q/4 (c) Q/3 and 2Q/3 (d) E and (Q – e), where e = electronic charge 27. Some point charges are placed on the circumference of circle at equal distance. (See fig.) The direction of electric field at centre O will be along- B(q) D (q) A(–q) O r q –q q –q (q)C (a) OA (b) OB (c) OC (d) OD 28. A small positively charged ball of mass m is suspended by an insulating thread of negligible mass. Another positively charged small ball is moved very slowly from a large distance until it is in the original position of the first ball. As a result, the first ball rises by h. How much work has been done? (a) mgh (b) 2 mgh (c) 3 mgh (d) 4 mgh 29. Two mutually perpendicular infinitely long lines of charge having charge per unit length as 1 and 2 are located in air at a distance "a" from each other. The force of interaction between them is– (a) 0 1 2 4   (b) 0 1 2 2a   (c) 0 1 2 2   (d) 0 1 2 4a   30. A little charged bead is inside the hollow frictionless sphere manufactured from the insulating material. Sphere has a diameter of 50 cm. The mass of the bead is 90 mg, its charge is 0.5 C. What minimum charge must carry an object at the bottom of the sphere to keep hold the charged bead at the vertex of the sphere in stable equilibrium? (a) 4.9 × 10–8 C (b) 9.8 × 10–8 C (c) 19.6 × 10–8 C (d) 30.2 × 10–8 C 31. Two uniformly long charged wires with linear densities  and 3 are placed along X and Y axis respectively. Determined the slope of electric field at any point on the line y = 3 x. (a) 3 3 (b) 3 2 3 (c) 3 3 1 (d) 3 32. Four charges + q each are located at the vertices of square ABCD of side a as shown in figure. Find the electric field E at the midpoint of side BC - A +q +q D P • +q C +q B (a) 2 2 0 q a 5 5 4  (b) 2 2 0 a q 5 5 4  (c) 0 (d) None of the above
33. Three charges each of +q, are placed at the vertices of an equilateral triangle. The charge needed at the centre of the triangle for the charges to be in equilibrium is – (a) 3 −q (b) – 3q (c) 3q (d) – 34. Two identical balls each having a density 1.6 gcm–3 are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle 30° with vertical. Now both the balls are immersed in a liquid of density 0.8 gcm–3 , but the angle does not change. The dielectric constant of the liquid is- (a) 1 (b) 2 (c) 3 (d) 4 35. Two concentric conducting spheres of radii r1 and r2 (r1< r2) carry electric charges of + Q and – Q respectively. The region between the sphere is filled with two insulating layers of dielectric constant 1 and 2 and width d1 and d2 respectively. Variation of potential and electric field with radial distance from O is given. Select the correct one. (assume Vat r2 = 0) O +Q –Q r2 r1 d2 d1 (a) r r 1 V r r1+d1 2 (b) r1 r E r r1+d1 2 (c) r1 r V r r1+d1 2 (d) r1 r E r r1+d1 2 36. Two charges of –4C and +4C are placed at points A (1,0,4) and B (2, –1,5) located in an electric field → E = 0.20 i ˆ V/cm. The torque acting on the dipole is - (a) 8 × 10–5 N-m (b) 8/ 2 × 10–5 N-m (c) 8 2 × 10–5 N-m (d) 2 2 × 10–5 N-m 37. Three concentric spherical metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities , –  and  respectively. If the shells A and C are at same potential, then the correct relation between a, b and c is - (a) a + c = b (b) b + c = a (c) a – b = c (d) a + b = c 38. An electric charge 10–3C is placed at origin (0, 0). Two points A and B are situated at ( 2 ̧ 2 ) and (2, 0) respectively. The potential difference between the points A and B will be– (a) 9 volts (b) zero (c) 2 volts (d) 4.5 volts 39. Anelectricdipoleis placed at anangle of 30o to a non-uniform electric field. The dipole experiences - (a) A torque as well as a translational force (b) A torque only (c) A translational forcé only in the direction of field (d) A translational forcé only in a direction normal to the direction of the field 40. Charges are placed on the vértices of a square as shown. Let → E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then – q q –q –q A B D C (a) → E remains unchanged, V changes (b) Both → E and V changes (c) → E and V remains unchanged (d) → E changes, V remains unchanged 41. The potential at a point x due to some charge is given by equation V(x) = (x 4) 20 2 − volts. Then electric field at x =4 is given by - (a) 3 5 volt/m and in the –ve x direction (b) 3 5 volt/ m and in the +ve x direction (c) 9 10 volt/m and in the –ve x direction (d) 9 10 volt/m and in the +ve x direction 42. Two thin rings each of radius R are placed at a distance 'd' apart. The charges on the rings are +q and –q. The potential difference between their centres will be– + + + + + – – – – – +q –q R d R (a) 2 4 0d qR  (b) 0 2 q          + − 2 2 R d 1 R 1 (c) Zero (d) 0 4 q          + − 2 2 R d 1 R 1 3q