Innovation Electrostatics

Electrostatics 1.

Two concentric spherical shell of radius a and 2a carry charges Qo and \u2212Qo. The switch S is closed at t = 0. The charge on the inner shell at time t is : (a) Q e o

\ue000

(a)

(b)

(c)

(d)

t

8 \ue002\ue001 aR 0 t

(b) Q e o

\ue000 4 \ue002\ue001 aR

(c) Q e o

0

\ue000

t

2 \ue002\ue001 aR 0

(d) zero 2.

5. In the above question, heat produced in the connecting wire is given by : 2 2 Q0 Q0 (a) (b) 8\ue006\ue003 4\ue006\ue003 0 a 0 a 2

(c)

3.

16\ue006\ue003 0 a

2

(d)

Q0 2\ue006\ue003 0 a

A non\ue001conducting 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 : (a) (c)

4.

Q0

QE ML QE 2ML

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 :

(b)

9QE 2ML

(d) zero

(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

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 7. radially outwards is taken positive then variation of electric field with distance x from centre is best represented by :

In above question, if C \ue004 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

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

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8.

The figure shows a infinitely long linear charge distribution of density \u03bb C/m along y\u2212axis. 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\u2212y plane. Assume gravity free space. (a) (c)

9.

\ue005 q\ue000 1\ue000 2l n3 \ue001 2\ue006\ue003 0 m

(b)

\ue005 l q n3 (d) 0 m \ue006\ue003

\ue005 q 2\ue006\ue003 0 m \ue005 l q n3 2 0 m \ue006\ue003

A ring with charge Q uniformly distributed over it, is fixed in y \ue001z plane with its centre at origin. A charge particle 3 R along x\ue001axis. When the particle reached Q, its minimum possible speed will be :

(c)

Qq \ue003 mR 0 3Qq 4\ue006\ue003 0 mR

(b) (d)

Qq

(d)

2\ue006\ue003 0 mr

Qq

\ue006\ue003 0 mr

12. In the above question if: \ u e 0 0 7 = 0, path will be straight line (a) (b) \ue007 = 90o, path will be parabolic but particle will not escape (c) \ue007 = 90o path will be parabolic and particle will escape (d) 0o < \ue007 < 90o will be parabolic and particle will escape 13. What should be the value of the velocity of charge q (say v2) and \ue007, so that the kinetic energy of the particle does not change? (a) (c)

is projected from x =

(a)

(c)

Qq

o

, 60

(b)

o

(d)

4\ue006\ue003 0 mr Qq

,90

2\ue006\ue003 0 mr

Qq

o

,90

4\ue006\ue003 0 mr Qq

o

,0

2\ue006\ue003 0 mr

14. If the particle is projected with velocity smaller than v2 and \ue007 = 90o, the path of the particle will be represented by : (a)

(b)

(c)

(d)

Qq 4\ue006\ue003 0 mR 3Qq

\ue006\ue003 0 mR

10. A non\ue001conducting semicircular 15. If the particle is projected with velocity greater than v 2 ring of radius R, contains but smaller than v1 with \ue007 =900, then the path of the charge Q and \ue001Q as shown in particle will be represented by: figure. What work is required to rotate the semi\ue001ring surviving slowly by an angle \ue006/2. (a) (b) 4QRE (a) 4QRE (b)

\ue006

(c)

2QRE

\ue006

(d) 2QRE

11. A point charge \u2018Q\u2019 is fixed at a point and another point charge \u2018\ue001q\u2019 of mass \u2018m\u2019 is projected with velocity v at angle \ue007 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? (a)

Qq 4\ue006\ue003 0 mr

(b)

2Qq

\ue006\ue003 0 mr

(c)

(d)

16. The semicircular non\ue001conducting ring of radius R containing +ve and negative charge as shown are joined in two perpendicular planes. The magnitude of linear charge densities is \ue005. The electric field at O will be :

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

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(a) (c)

\ue005 2\ue006\ue003 0 R

(b)

\ue005

2\ue005

r

then net force on the loop will be : (a) \ue005\ue006RE (b) 2\ue005\ue006RE (d) zero

2\ue005\ue006 RE

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 ?

18. In above question, the magnitude of torque acting on the loop will be : (b) 2\ue005R2E \ue005R2E (a) (c)

2\ue005 R 2

(d)

(d) zero

2\ue006\ue003 0R

c6 17. In above question if an electric field exists, E \ue002 E0 \u i 02

(c)

(c)

\ue006\ue003 0R

E

(d) 2 2\ue005 R 2

(a)

(b)

E

19. Charge Q is uniformly distributed over volume of a non \ue001conducting sphere of radius R and dielectric constant(c) k. The variation of electric field with the distance x from the center of sphere is correctly represented by : (a)

(c)

(b)

(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\ue001 component of force as a function of time varies as : (a)

(b)

(c)

(d)

24. Two infinitely long and uniformly charged wires linear charge (with density \ue005) are fixed in x\ue001 y plane at x = \ue008a 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

\ue005 (a) \ue006\ue003 ag 0

\ue005 (b) 2\ue006\ue003 0 ag 2

2

2\ue005

(c) \ue006\ue003 21. In above question variation of x\ue001component of force as 0 ag a function of time varies as : (a) (b)

(d)

\ue005 2\ue006\ue003 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 5.C 6.B 7.B 8.A 9.B 10.B 11.C 12.A,C,D 16.C 17.D 18.B 19.D 20.D 21.C 22.B 23.C 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