CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAIIIT – JEE-2014 TW TEST MARKS: 60
TIME: 1 HR TOPIC: ELECTROSTATISTICS DATE: 29/04/13 SINGLE CHOICE QUESTIONS (+3, –1)
1. A spherical charged conductor has surface density of charge as . The electric field intensity on its surface is E. If the radius of surface is doubled, keeping unchanged , what will be the electric field intensity on the new sphere?
(a) E 2 (b) E 4 (c) 2E (d) E
2. Charge Q is given a displacement raiˆb jˆ in an electric field EE i1ˆE j2ˆ. The work done is
(a) Q E a
1 E b2
(b) Q
E a1
2
E b2
2(c) Q E
1E2
a2b2 (d) Q
E12E22
2 a2b23. An insulated sphere of radius R has a uniform volume charge density . The electric field at a point P inside the sphere at a distance r from the centre is
(a) 0 R 3 (b) 0 r 3 (c) zero (d) 0 2 r 3
4. Consider two concentric spherical surfaces S1with radius a and S2with radius 2a, both centred on the origin. There is a charge qat the origin, and no other charges. Compare the flux 1 , through S1
with the flux 2 through S2.
(a) 1 4 2 (b) 1 2 2 (c) 1 2 (d) 1 2 2
5. If the flux of the electric field through a closed surface is zero, then (a) the electric field must be zero everywhere on the surface . (b) the total charge inside the surface must be zero.
(c) the electric field must be uniform throughout the closed surface. (d) the charge outside the surface must be zero.
6. Two particles A and B (B is right of A) having charges 8 10 6C and 2 106C, respectively, are held fixed with separation of 20 cm . Where should a third charged particle be placed so that it does not experience a net electric force.
(a) 5 cm right of B (b) 5 cm left of A (c) 20 cm left of A (d) 20 cm right of B
7. A point charge of 100 C is placed at
3iˆ4 j mˆ
. Find the electric field intensity due to this charge at a point located at
9i 12 j mˆ ˆ
.(a) 8000 Vm1 (b) 9000 Vm1 (c) 2250 Vm1 (d) 4500 V m1
8. It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?
(a) q
1 2 2
2 (b) q
1 2 2
2 (c)
q 1 2 2 4 (d)
q 1 2 2 4 9. Four identical charges Q are fixed at the four corners of a square of side a. The electric field at a point P located symmetrically at a distance a 2from the centre of the square is
(a) 2 0 Q 2 2 a (b) 2 0 Q 2 a (c) 2 0 2 2Q a (d) 2 0 2Q a
10. A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius
3Rat a distance of R from the centre of the shell. Find the electric potential at the centre of the shell (a) 0 1 q 4 2R (b) 0 1 4q 4 3R (c) 0 1 4 5q 6R (d) 0 1 2q 4 3R
11. We have three identical metallic spheres A,B and C.A is given a charge Q and B and C are uncharged. The following processes of touching of two spheres one carried out in succession. Each process is carried out with sufficient time:
(i) A and B (ii) B and C (iii) C and A (iv) A and B (v) B and C The final charges on the sphere are
(a) 11Q 5Q 11Q, 32 16 32 (b) 11Q 11Q 5Q , 32 32 16 (c) 8Q 5Q 5Q , , 8 16 16 (d) 5Q 11Q 11Q , , 16 32 32
12. A non-conducting sphere with a cavity has volume charge density .O1 and
2
O represent the two centres as shown. The electric field inside the cavity is
0
E . Now, an equal and opposite charge is given uniformly to the sphere on its outer surface. The magnitude of electric field inside the cavity becomes
(a) zero (b) E0 (c) 2E0 (d) 3E0
13. A conducting spherical shell is earthed. A positive charge q1 is placed at the centre and another small positive charge q2is placed at a distance
r from q1(see figure). Ignore the effect of induced charge due to q2 on the sphere. Then the coulomb force on q2is
(a) zero (b) 1 2 2 q q 4r (c)
1 2 2 0 q q 4 rR (d)
1 2 2 2 0 q q 4 r R14. Consider a system of three charges q 3, q 3 and 2q 3 placed at points A,B and C, respectively, as shown in Figure. Take Oto be the centre of the circle of radius R and angle CAB60. Then
(a) the electric field at point Ois q 80R2 directed along the negative x axis
(b) the potential energy of the system is zero
(c) the magnitude of the force between the charges at C and B is q2 540R2 (d) the potential at point Ois q 120R
15. A uniformly charged thin spherical shell of radius R carries uniform surface charge density of per unit area. It is made of two hemispherical shells, held together by pressing them with force F. F is proportional to (a) 2 2 0 1 R (b) 2 0 1 R (c) 2 0 1 R (d) 2 2 0 1 R
16. Three concentric metallic spherical shells of radii R, 2R, 3R are given charges
1 2 3
Q , Q , Q , respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells Q : Q : Q1 2 3 is
(a) 1: 2 : 3 (b) 1: 3: 5
(c) 1: 4 : 9 (d) 1: 8 :18
COMPREHENSION TYPE (+3, –1)
The electric potential varies in space according to the relation V 3x4y. A particle of mass 0.1kg starts from rest from point
2,3.2
under the influence of this field. The charge on the particle is 1C
. Assume V and
x, y
are in S.I. units17. The component of electric field in the x direction
Ex
is(a) 3Vm1 (b) 4 Vm1 (c) 5Vm1 (d) 8Vm1
18. The component of electric field in the y direction
Ey is(a) 3Vm1 (b) 4 Vm1 (c) 5Vm1 (d) 8Vm1
19. The time taken to cross the x axis is
(a) 20 s (b) 40 s (c) 200 s (d) 400 s
20. The velocity of the particle when it crosses the x axis is
(a) 20 10 3ms1 (b) 40 10 3ms1 (c) 30 10 3ms1 (d) 50 10 3ms1
3R
2R R
CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA
ANSWER KEY 1. (d) 2. (a) 3. (b) 4. (a) 5. (b) 6. (d) 7. (b) 8. (d) 9. (b) 10. (c) 11. (d) 12. (b) 13. (a) 14. (c) 15. (a) 16. (b) 17. (a) 18. (b) 19. (d) 20. (a)ELECTROSTATISTICS SOLUTION 1. (d)
0
E
does not depend upon radius if is constant
2. (a) WF.r qE.r 3. (b)
3 3 3 0 0 4 3 R r kQr 1 r E 4 3 R R 4. (a) 5. (b) in in in 0 0 q q 0 q 0 6. (d) 20cm B x 6 8 10 C 2 106C Q ALet the third charge Q be placed at a distance x to the right of B. Then
6
6 2 2 kQ 2 10 kQ 8 10 x 20 x x20 cm 7. (b)
ˆ
ˆ ˆ ˆ r 9 3 i 12 4 j 6i 8 j r 6282 10 m 9 6 1 2 9 10 100 10 E 9000 Vm 10 8. (d) 2 AC l BD 1 2 BO
cos 45 BO BD BA BC F F F F Solving, we get
1 2 2 ,
4 q Q Q should be negative of q O Q D q C q A BO F q BC F FBD B FBA9. (b) net 2 2 0 0 4 Q 1 Q E 4E cos 4 a 2 2 a 10. (c) q q q R 2R3R 6q 3q 2q 6R 11. (d)
(i) Q 2, Q 2, 0 (ii) Q 2, Q 4, Q 4 (iii) 3Q 8, Q 4,3Q 8
(iv) 5Q 16,5Q 16,3Q 8 (v) 5Q 16,11Q 32,11Q 32
12. (b)
Electric field will remain the same, because electric field due to surface charge distributed uniformly will be zero at any point inside sphere.
13. (a)
There is no charge on the outer surface. Hence, no force on q 2
14. (c)
2 BC 2 2 0 0 q 2q 1 3 3 q F 4 R 3 54 R 15. (a) Pressure 2 0 2 and force 2 2 0 R 2 16. (b)
1 2 3 1 1 2 2 2 2 Q Q Q Q Q Q 4 R 4 2R 4 3R Q : Q : Q ::1: 3 : 5 1 2 3 E P a Q O a 2 a 2 Q Q Q Q a B A D C O 2R q 3R17. (a) 18. (b) 19. (d) 20. (a) 1 1 x y V y E 3Vm ; E 4Vm x y 6 5 2 x x qE 1 10 3 a 3 10 ms m 0.1 6 y 5 2 y qE 1 10 4 a 4 10 ms m 0.1
Time taken to cross the x axis Using s ut 1at2 2 5 2 1 3.2 4 10 t 2 t400 s 5 x a tx 3 10 400 12 10 ms 3 1 5 y a ty 4 10 400 16 10 3ms1 2 2 x y 3 1 20 10 ms
