Innovation Electrostatics

Electrostatics 1.

Two concentric spherical shell of radius a and 2a carry charges Qo and −Qo. The switch S is closed at t = 0. The charge on the inner shell at time t is : (a) Q e o



(b) Q e o (c) Q e o (d) zero 2.

3.

(c)

(d)

t 2 0 aR

Q02 16 0 a

(d)

QE 2ML

5.

Q20 2 0 a

A nonconducting rod carries charge Q uniformly distributed over half of its length. The rod has mass m and length L. It can rotate about one of its ends O. Assuming gravity free space, the angular velocity of rod when it becomes vertical is : QE 9QE (a) (b) ML 2ML (c)

4.

t 4 0 aR

In the above question, heat produced in the connecting wire is given by : Q02 Q20 (a) (b) 8 0 a 4 0 a (c)

(b)

t 8 0 aR





(a)

(a)

(b)

(c)

(d)

6.

A light conducting sphere suspended by an insulating thread is in contact with an uncharged metal sphere B, which is fixed on an insulating stand. If a negatively charged sphere C is through very close to B without touching it, then : (a) A will remain in same position (b) A will move away from B (c) A will be attracted more strongly by B (d) None

7.

In above question, if C  is touched with B and removed away then : (a) A will remain in same position (b) A will move away from B (c) A will be attracted more strongly by B (d) None

(d) zero

The figure shows three concentric conducting shells of radius R, 2R and 3R. The innermost shell is earthed and the middle shell is given a charge Q. The outer shell can be earthed by switch S. If radially outwards is taken positive then variation of electric field with distance x from centre is best represented by :

Two similar conducting plates are given equal and opposite charge and placed as shown in figure. Which of the following diagram best represent the electric lines of forces :

INNOVATIONS, by Er Sunil Kumar Singh. www.physicswithsunilsingh.blogspot.com

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8.

(a) (c)

9.

(c)

The figure shows a infinitely long linear charge distribution of density λ C/m along y−axis. A point charge q of m is tied to a thread which other end is fixed at x = 2L. What should be minimum velocity v so that the charge may complete a circle about O in x−y plane. Assume gravity free space. q  1  2l n3 2 0 m ql n3  0 m

3Qq 4 0 mR

(b)

q 2 0 m

(d)

ql n3 2 0 m

(d)

(d)

Qq  0 mr

12. In the above question if: (a)  = 0, path will be straight line (b)  = 90o, path will be parabolic but particle will not escape (c)  = 90o path will be parabolic and particle will escape (d) 0o <  < 90o will be parabolic and particle will escape

A ring with charge Q uniformly distributed over it, is fixed in yz plane with its centre at origin. A charge particle is projected from x = 3 R along xaxis. When the particle reached Q, its minimum possible speed will be : Qq Qq (a) (b)  0 mR 4 0 mR (c)

Qq 2 0 mr

3Qq  0 mR

10. A nonconducting semicircular ring of radius R, contains charge Q and Q as shown in figure. What work is required to rotate the semiring surviving slowly by an angle /2. 4QRE (a) 4QRE (b)  2QRE (c) (d) 2QRE  11. A point charge ‘Q’ is fixed at a point and another point charge ‘q’ of mass ‘m’ is projected with velocity v at angle  with the line joining them. With what minimum velocity (say v1) should the charge be projected so that it may escape from attraction field of Q? Qq 2Qq (a) (b) 4 0 mr  0 mr

13. What should be the value of the velocity of charge q (say v2) and , so that the kinetic energy of the particle does not change? Qq Qq , 60o ,90o (a) (b) 4 0 mr 4 0 mr (c)

Qq ,90o 2 0 mr

(d)

Qq , 0o 2 0 mr

14. If the particle is projected with velocity smaller than v2 and  = 90o, the path of the particle will be represented by : (a)

(b)

(c)

(d)

15. If the particle is projected with velocity greater than v 2 but smaller than v1 with  =900, then the path of the particle will be represented by: (a)

(b)

(c)

(d)

16. The semicircular nonconducting ring of radius R containing +ve and negative charge as shown are joined in two perpendicular planes. The magnitude of linear charge densities is . The electric field at O will be :

INNOVATIONS, by Er Sunil Kumar Singh. www.physicswithsunilsingh.blogspot.com

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(a) (c)

 2 0 R

(b)



2 0 R

(d)

(d) zero

2  0 R

r 17. In above question if an electric field E  E 0 ˆi exists, then net force on the loop will be : (a) RE (b) 2RE (c) (d) zero 2RE 18. In above question, the magnitude of torque acting on the loop will be : (a) R2E (b) 2R2E (c) (d) 2 2R 2 E 2R 2 E 19. Charge Q is uniformly distributed over volume of a non conducting sphere of radius R and dielectric constant k. The variation of electric field with the distance x from the center of sphere is correctly represented by : (a)

(c)

(b)

(c)

22. The diagram shows an arrangement of four evenly spaced parallel metal plates. Which of following graph best represent the variation of potential V with position r ? (a)

(b)

(c)

(d)

23. The variation of electric field strength E with position r is best represented by : (a)

(b)

(c)

(d)

(d)

20. The diagram shows two fixed spheres P and Q which carry equal but opposite charges. A third charged sphere R is moved with a constant velocity in the shown direction. The variation of y component of force as a function of time varies as : (a)

(b)

(c)

(d)

21. In above question variation of xcomponent of force as a function of time varies as : (a) (b)

24. Two infinitely long and uniformly charged wires (with linear charge density ) are fixed in x y plane at x = a as shown in figure. Another similar wire is hanging freely in the symmetric plane between the wires. The maximum possible linear mass density of this wire will be: 2 2 (a) (b) 0 ag 2 0 ag (c)

2 2 0 ag

(d)

 2 0 ag

INNOVATIONS, by Er Sunil Kumar Singh. www.physicswithsunilsingh.blogspot.com

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25. A point charge is placed at the center of a non− conducting sphere of radius R and of dielectric constant k. Which of the following plot best represents the variation of electric field with distance r from the point charge. (a)

(b)

(c)

(d)

Answers 1.A 13.B

2.C 14.B

3.B 15.C

4.A 16.C

5.C 17.D

6.B 18.B

7.B 19.D

8.A 20.D

9.B 21.C

10.B 22.B

11.C 23.C

12.A,C,D 24.B 25.C

INNOVATIONS is a series of topic wise fresh problems framed exclusively by Er Sunil Kumar Singh for students preparing for IITJEE.

INNOVATIONS, by Er Sunil Kumar Singh. www.physicswithsunilsingh.blogspot.com