आिधका�रक और सामान्य प्र�

1. A uniform electric field having a magnitude E0 and direction along the positive X-axis exists. If the potential V is zero at x=0, then its value at x = +x will be (a) V(x) =+xE0 (b) V(x) =-xE0 (c) V(x) =+x2E0 (d) V(x) =-x2E0

2. The magnitude of electric field E

in the angular region of a charge cylindrical capacitor (a) is same throughout (b) is higher near the outer cylinder than near the inner cylinder (c) varies as 1/r, where r is the distance from the axis (d) varies as 1/r2, where r is the distance from the axis.

3. Two charges –10C and +10 C are placed 10 cm aprt. Potential at the centre of the line joining the two charges is (a) zero (b) 2 V (c) – 2V (d) none of these.

4. Equal charges q each are placed at the vertices A and B of an equilateral triangle ABC of side a. The magnitude of electric intensity at the point C is

(a) 204

qa∈π

(b) 204q2a∈π

(c) 204q3a∈π

(d) 204

2qa∈π

5. There is an electric field E in X-direction. If work done in moving a charge 0.2 through a distance of 2m along a line making an angle of 60 degree with X-axis is 4.0 joule, what is the value of E? (a) 3 newton per coulomb (b) 4 newton per coulomb (c) 5 newton per coulomb (d) none of these.

6. Two insulated charge conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10 µ C are connected by a copper wire and then they are separated. Then (a) Both spheres will have equal charges (b) Surface charge density on the 20cm sphere will be greater than that on the 15 cm sphere (c) Surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere (d) Surface charge density on the two spheres will be equal

7. Two condensers C1 and C2 in a circuit are joined as shown in Fig. The potential of point A is V1 and that of B is V2. The potential of point D will be

(a) 21 (V1+V2) (b)

21

1221CC

VCVC++

(c) 21

2211CC

VCVC++ (d)

21

2112CC

VCVC+−

8. Two spherical conductors each of capacity C are charged to potential V and –V. These are then connected by mean of a fine wire. The loss of energy is

(a) zero (b) 21 CV2 (c) CV2 (d) 2 CV2

9. An air capacitor of capacity C=10µ f is connected to a constant voltage battery of 12 volt. Now the space between the plates is filled with a liquid of dielectric constant 5. The (additional) charge that flows now from battery to the capacitor is (a) 120 µC (b) 600 µC (c) 480 µC (d) 24 µC

10. Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If p is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then the potential at the point P is given by (r>>2a)

(a) V= 204

cos pr∈πθ

(b) V=r04

cos p∈π

θ

(c) V=r04

sn p∈πθ

(d) V= 204

cos pr∈πθ

11. A point charge q is placed at a distance 2a directly

above the centre of a square of side a. The electric flux through the square is

(a) 0

q∈

(b) 0

q∈π

(c) 04

q∈

(d) 06

q∈

12. An uncharged capacitor is connected to a battery. On charging the capacitor, (a) all the energy supplied is stored in the capacitor (b) half the energy supplied is stored in the capacitor (c) the energy stored depends upon the capacity of the capacitor only (d) the energy stored depends upon the time for which the capacitor is charged

13. In Milikan’s oil drop experiment, an oil drop carrying a charge O is held stationary by a potential difference of 2400 volt between the plates. To keep a drop of half the radius stationary the potential difference had to be made

A, V1 B, V2 C1 C2

D

Prof. Sanjib Nanda. M.Sc.M.Phil. Physics (Gold Medallist) 9317931711

600 volt. What is charge on the second drop

(a) 4Q (b)

2Q (c) Q (d)

23Q

14. A parallel plate capacitor of plate area A and plate separation d is charge to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and work done by the system in question, in the process of inserting the slab, then select the incorrect relation from the following:

(a) Q=dAV0∈ (b) E=

KdV

(c) W=Kd2AV2

0∈ (d)W=2dAV2

0∈

−

K11

15. A 10 µ F capacitor and a 20 µ F capacitor are connected in series across 200 V supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor?

(a) 9

800 volt (b) 3

800 volt

(c) 400 volt (d) 200 volt 16. An electric dipole is placed along the X-axis at the

origin O. A point P is at a distance of 20 cm from

this origin such that OP makes an angle 3π with

the X-axis. If electric field at P makes an angle π with X-axis, the value of θ is

(a) 3π (b)

3π +tan-1

23 (c)

23π (d) tan-1

23

17. Two equal charges, q each are placed at a distance of 2a, and a third charge –2q is placed at the mid-point. The potential energy of the system is

(a) a0

2

8q∈π

(b) a0

2

86q∈π

(c) a0

2

87q-∈π

(d) a0

2

89q∈π

18. To obtain 3µF capacity from three capacitors of 2µF each they will be arranged (a) all three in series (b) all three in parallel (c) two capacitors in series and the third in parallel with combination of first two (d) two capacitors in parallel and the third in series with combination of first two

19. A dielectric slab of thickness d is inserted in a paralle plate capacitor whose negative plate is at X=0 and positive plate is at X=3d. The slab is equidistant from the plates. The capacitor is given some charge. As X goes from 0 to 3d (a) the electric potential increases at first, then decreases and again increases

(b) the electric potential increases continuously (c) the direction of the electric field remains the same (d) the magnitude of the electric field remains the same

20. A positively charged thin metal ring of radius R is fixed in X-Y plane with its centre at the origin O. A negatively charged particle P is released from rest at the point (0, 0, Z0) where (Z0>0). Then the motion of P is (a) periodic for all values of Z0 satisfying 0<Z0<∞ (b) simple harmonic for all values of Z0 satisfying 0<Z0 ≤R (c) approximately simple harmonic provided Z0<<R (d) such that P crosses O and continues to move along the negative Z-axis towards Z=-∞

21. A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre (a) increases as r increases for r<R (b) decreases as r increases for 0<r<∞ (c) decreases as r increases for R<r<∞ (d) is discontinuous at r=R

22. A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then the electric intensity E at Q is proportional to (a) E-1 and r-2 (b) E and r-2 (c) E2 and r-3 (d) E and r-3

23. A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is (a) qEy2 (b) qE2y (c) qEy (d) q2Ey

24. Number of electrons in one coulomb of charge will be (a) 5.46× 1029 (b) 6.25× 1018 (c) 1.6× 10+19 (d) 9× 1011

25. Equal charges are given to two conducting spheres of different radii. The potential will (a) be more on the smaller sphere (b) be more on the bigger sphere (c) be equal on both the sphere (d) depends on the nature of the materials of the sphere

26. Eight dipoles of charges of magnitude e are placed inside a cube. The total electric flux coming out of the cube will be

(a) 0

8∈

e (b) 0

16∈

e (c) 0∈

e (d) zero

27. A parallel, condenser with oil between the plates (dielectric constant of oil K=2) has a capacitance C. If the oil is removed, then capacitance of the

Prof. Sanjib Nanda. M.Sc.M.Phil. Physics (Gold Medallist) 9317931711

capacitor becomes

(a) 2C (b)

2C (c) 2 C (d) 2 C

28. In bringing an electron towards another electron, the electrostatic potential energy of the system (a) remains same (b) becomes zero (c) increases (d) decreases

29. When air is replaced by dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance (a) increases K-1 times (b) increases K times (c) remains unchanged (d) decreases K times

30. What is effective capacitance between points X and Y in fig.? (a) 6 µF (b) 12 µ F (c) 18 µF (d) 24 µF

31. If a slab of insulating material 4× 10-5 m thick is introduced between the plates of a parallel plate capacitor, the distance between the plates has to be increased by 3.5 × 10-5 m to restore the capacity to original value. Then the dielectric constant of the material of slab is (a) 8 (b) 6 (c) 12 (d) 10

32. If electric field in a region is radially outward with magnitude E=Ar, the charge contained in a sphere of radius r centered at the origin is

(a) 30

0Ar

41∈π

(b) 4π∈0Ar3

(c) 300 rA

41∈π

(d) 30

0 A4r∈π

33. Two spheres of radii R1 and R2 respectively are charged and joined by a wire. The ratio of electric field of spheres is (a) 2

122 R/R (b) 2

221 R/R

(c) R2/R1 (d) R1/R2 34. Two metal pieces having a potential difference of

800 V are 0.02 m apart horizontally. A particle of mass 1.96× 10-15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is (a) 8e (b) 6e (c) 3e (d) e

35. A 2µ F capacitor is charged to 100 volt and then its plates are connected by a conducting wire. The heat produced is (a) 0.001 J (b) 0.01 J (c) 0.1 J (d) 1J

36. A parallel plate capacitor has the space between

its plates filled by two slabs of thickness 2d each

and dielectric constant K1 and K2 d is the plate separation of the capacitor. The capacity of the capacitor is

(a)

+∈

21

210

KKKK

Ad2 (b)

+

∈

21

210

KKKK

dA2

(c) A

d2 0∈ (K1+K2) (d)

+∈

21

210

KKKK

dA2

37. The electric potential V is given as a function of distance x (metre) by V=(5x2+10x-4) volt. Value of electric field at x=1m is (a) –23 V/m (b) 11 V/m (c) 6 V/m (d) –20 V/m

38. Two infinite plane, parallel sheets, separated by a distance d have equal and opposite uniform charge densities σ . Electric field at a point between the sheets is (a) Depends upon location of the point

(b) 02∈

σ (c) 0∈σ (d) Zero

39. A 10 µ F capacitor is charged to a potential difference of 50 V and is connected to another uncharged capacitor in parallel. Now the common potential difference becomes 20 volt. The capacitance of second capacitor is (a) 15 µF (b) 30 µF (c) 20 µF (d) 10 µF

40. A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitors is parallel. The energy in each of the capacitors is (a) 3 U/2 (b) U (c) U/4 (d) U/2

41. A semi-circular arc of radius ‘a’ is charged uniformly and the charge per unit length is λ. The electric field at its centre is

(a) 202 a∈πλ (b)

a04∈λ (c)

a0

2

2 ∈πλ (d)

a02 ∈πλ

42. Two capacitors A and B are connected in series with a battery as shown in Fig. 12.58. When the switch S is closed and the two capacitors get charged fully, then a) the potential difference across the plates of A is 4V and across the plates of B is 6 V (b) the potential difference across the plates of A is 6 V and across the plates of B is 4 V (c) the ratio of electrical energies stored in A and B is 2:3 (d) the ratio of charges on A and B is 3:2

43. In a non-uniform electric field, electric dipole experiences (a) torque only(b) torque as well as net force (c) force only (d) none of these

44. An α-particle and a proton are accelerated through same potential difference from rest. Find the ratio of their final velocity (a) 2 :1 (b) 1:1 (c) 1: 2 (d) 1:2

S 10 V

2 µF 3 µF

A B

Prof. Sanjib Nanda. M.Sc.M.Phil. Physics (Gold Medallist) 9317931711

45. Hollow spherical conductor with a charge of 500 µC is acted upon by a force 562.5 N. What is E at its surface? (a) zero (b) 1.125× 106 N/C (c) 2.25× 106 N/C (d) 4.5× 106 N/C

46. A uniform electric field pointing in positive y-direction exists in a region. Let A be the origin, B be the point on the x-axis at x=2 cm and C be the point on the y-axis at y=2 cm. Then the potentials at the points A, B and C satisfy: (a) VA<VB (b) VA>VB (c) VA<VC (d) VA>VC

47. Consider the situation shown in the figure. The capacitor A has a charge q on it whereas B is uncharge. The charge appearing on the capacitor B a long time after the switch is closed is (a) zero (b) q/2 (c) q (d) 2q

48. The equivalent capacitance in the circuit shown b/w pts A and B will be (a) 10/3 µF (b) 4mF (c) 6µF (d) 8µF

49. A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x=axis at x=+1cm and C be the point on the y-axis at y=+1cm. Then the potential at the point. A, B and C satisfy (a) VA<VB (b) VA>VB (c) VA<VC (d) VA>VC

50. A quantity X is given by 0∈ Lt∆

∆V , where 0∈ is the

permittivity of free space, L is a length, V∆ is potential difference and ∆ t is time interval. The dimensional formula for X is the same as that of (a) resistance (b) charge (c) voltage (d) current

51. A charge Q µC is placed at the centre of a cube, the flux coming out from any surface will be

(a) 6

010

6Q −×∈

(b) 3

010

6Q −×∈

(c) 024

Q∈

(d) 06

Q∈

52. A straight wire of length l and electric dipole moment p is bent to form a semicircle. The new dipole moment would be

(a) p/2 (b) π2p (c) p/2π (d) 2p

53. Electric field at the centroid of a triangle carrying q charge at each corner is

(a) zero (b) 2rKq2 (c) 2r

Kq2

1 (d) 2r3Kq

54. In Fig. as shown if net force on Q is

zero, the value of qQ is

(a) 2 (b) 2 2

(c) 22

1 (d) 2

1

55. A parallel plate capacitor is filled by copper plate of thickness b. The new capacity will be

(a) b-2d

A0∈ (b) b-dA0∈ (c)

b/2-dA0∈ (d)

dA0∈

56. A capacitor of capacity C1 charged to V volt is connected to an uncharged capacitor of capacity C2. The final potential difference across each will be

(a)21

2CCVC+

(b)21

1CC

VC+

(c)

+

1

2CC1 V(d)

1

2CC-1 V

57. Identical charges –q each are placed at 8 corners of a cube of each side b. Electrostatic potential energy of a charge +q which is placed at the centre of cube will be

(a) bq

0

224-∈π

(b) bq

0

228-∈π

(c) b

q

0

2

34-∈π

(d) b

q0

2

428∈π

58. If there are n capacitors in parallel connected to V volt source, then energy stored is equal to

(a) CV (b) CV2 (c) 2CV2n1 (d)

21 nCV2

59. On moving a charge of 20C by 2 cm, 2 joule of work is done, then the potential difference between the points is (a) 8 V (b) 2 V (c) 0.1 V (d) 0.5 V

60. Two point charges are +2C and +6C repel each other with a force of 12N. If a charge of –4C is given to each of these charges, the force now is (a) zero (b) 4 N attractive (c) 4 N repulsive (d) 12 N attractive

Q

Q

q

q

B

A

All 4 µF

A B

q

Prof. Sanjib Nanda. M.Sc.M.Phil. Physics (Gold Medallist) 9317931711