Numerical Problems of Electrostatics Class-12 Chapter-1

Numerical Problems of Electrostatics Class-12 Chapter-1

1. Three charges 4q, Q and q are in a straight line in the position of 0, l/2 and l respectively. The resultant force on q will be zero, if Q = 

(a) -q           (b) -2q           (c) -q/2        (d) 4q

2. Dielectric constant of pure water is 81. Its permittivity will be 

(a) 7.12 *  10-10     MKS units                 (b) 8.86 *  10-12     MKS units 

 (c) 1.02 *  1013     MKS units                 (d) Cannot be calculated

3. When 1014  electrons are removed from a neutral metal sphere, the charge on the sphere becomes 

(a) 16 μC     (b) -16 μC       (c) 32 μC        (d) -32 μC

4. The force between two charges 0.06 m apart is 5 N. If each charge is moved towards the other by 0.01m, then the force between them will become 

(a) 7.20 N       (b) 11.25 N       (c) 22.50 N         (d) 45.00 N

5. Two point charges +3 μC and +8 μC repel each other with a force of 40 N. If a charge of -5 μC is added to each of them, then the force between them will become  

(a) -10 N        (b) +10 N        (c) +20 N         (d) -20 N 

6. Two charges +4e and +e are at a distance x apart. At what distance, a charge q must be placed from charge +e so that it is in equilibrium 

 (a) x/2         (b) 2x/3         (c) x/3            (d) x/6

7. The electric field near a conducting surface having a uniform surface charge density σ is given by 

(a) σ/ε₀ and is parallel to the surface  

(b) 2σ/ε₀ and is parallel to the surface  

(c) σ/ε₀ and is normal to the surface 

(d) 2σ/ε₀ and is normal to the surface

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

9. Four charges are placed on corners of a square as shown in the figure having a side of 5 cm. If Q is one microcoulomb, then electric field intensity at the centre will be

10. Two point charges placed at a certain distance r in air exert a force F on each other. Then the distance r' at which these charges will exert the same force in a medium of dielectric constant k is given by

11. Two point charges of 20 μC and 80 μC are 10 cm apart. Where will the electric field strength be zero on the line joining the charges from 20 μC charge 

(a) 0.1 m     (b) 0.04 m       (c) 0.033 m        (d) 0.33 m

12. What is the potential energy of the equal positive point charges of 1 μC each held 1 m apart in air 

(a) 9 × 10-3  J    (b) 9 × 10-3  eV       (c) 2 eV/m        (d) Zero

13. An electron enters between two horizontal plates separated by 2mm and has a potential difference of 1000V. The force on electron is

(a) 8 × 10-12  N    (b) 8 × 10-14  N       (c) 8 × 109  N         (d) 8 × 1014  N 

14. Electric charges of +10 μC, +5 μC, -3 μC and +8 μC are placed at the corners of a square of side √2 m. the potential at the centre of the square is

(a) 1.8 V   (b) 1.8 × 106  V       (c) 1.8 × 105 V         (d) 1.8 × 104  V 

15. Two charges of 4 μC each are placed at the corners A and B of an equilateral triangle of side length 0.2 m in air. The electric potential at C is 

(a) 9 × 104  V    (b) 18 × 104  V       (c) 36 × 104  V         (d) 36 × 10-4  V 

16. Equal charges q are placed at the four corners A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be 

17. Two identical conductors of copper and aluminium are placed in identical electric fields. The magnitude of induced charge in the aluminium will be

(a) Zero     (b) Greater than in copper      (c) Equal to that in copper       (d) Less than in copper

18. Two equal charges q are placed at a distance of 2a and a third charge -2q is placed at the midpoint. The potential energy of the system is

19. Two point charges 100 μC and 5 μC are placed at points A and B respectively with AB = 40 cm. The work done by external force in displacing the charge 5 μC from B to C, where BC = 30 cm, angle 

ABC = 90°

(a) 9 J     (b) 81/20 J       (c) 9/25 J       (d) -9/4 J

20. 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 the charge on the particle is 

(a) e             (b) 3e           (c) 6e               (d) 8e

21. A proton is accelerated through 50,000 V. Its energy will increase by    

(a) 5000 eV      (b) J          (c) 5000 J        (d) 50,000 J

22. When a proton is accelerated through 1V, then its kinetic energy will be  

(a) 1840 eV      (b) 13.6 eV        (c) 1 eV       (d) 0.54 eV

23. What is the magnitude of a point charge which produces an electric field of 2 N/coulomb at a distance of 60 cm 

(a) 8 × 10-11 C      (b) 2 × 10-12C     (c) 3 × 10-11C     (d) 6 × 10-10C

24. Two charges +5 μC and +10 μC are placed 20 cm apart. The net electric field at the mid-Point between the two charges is 

(a) 4.5 × 106 N/C directed towards +5 μC

(b) 4.5 × 106 N/C directed towards +10 μC

(c) 13.5 × 106 N/C directed towards +5 μC

(d) 13.5 × 106 N/C directed towards +10 μC

25. As shown in the figure, charges +q and -q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is 

26. A charged particle of mass 5 × 10-5 C is held stationary in space by placing it in an electric field of strength 107 NC-1  directed vertically downwards. The charge on the particle is  

(a) -20 × 10-5 μC                    (b) -5 × 10-5 μC             (c) 5 × 10-5  μC           (d) 20 × 10-5 μC

27. Three charges Q, +q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to 

28. The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be 

(a) 2V              (b) 4V           (c) 8V            (d) 16V

29. Two spheres A and B of radius 'a' and 'b' respectively are at the same electric potential. The ratio of the surface charge densities of A and B is 

30. In a hydrogen atom, the electron revolves around the nucleus in an orbit of radius 0.53 × 10-10 m. Then the electrical potential produced by the nucleus at the position of the electron is 

(a) -13.6 V         (b) -27.2 V        (c) 27.2 V         (d) 13.6 V

31. Electric potential at any point is

, then the magnitude of the electric field is 

32. A drop of 10-6 kg water carries 10-6 C charge. What electric field should be applied to balance its weight (assume g = 10 ms-2 )

(a) 10 V/m upward        (b) 10 V/m downward       (c) 0.1 V/m downward         (d) 0.1 V/m upward

33. A charged particle of mass 0.003 gm is held stationary in space by placing it in a downward direction of the electric field of 6 × 104  N/C. Then the magnitude of the charge is 

(a) 5 × 10-4 C      (b) 5 × 10-10 C       (c) -18 × 10-6 C          (d) -5 × 10-9 C

34. An alpha-particle is accelerated through a potential difference of 200V. The increase in its kinetic energy is 

(a) 100 eV         (b) 200 eV            (c) 400 eV                  (d) 800 eV 

35. A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be  

(a) 1840 keV         (b) 1/1840 keV           (c) 1 keV             (d) 920 keV 

36. A conducting sphere of radius R = 20 cm is given a charge of 16 μC . What is E at centre  

(a) 3.6 × 106  N/C         (b) 1.8 × 106  N/C             (c) Zero              (d) 0.9 × 106  N/C

37. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point p at distance R/2 from the centre of the shell is

38. An electron enters in a high potential region from a lower potential region then its velocity  

(a) Will increase                                      (b) Will change in direction but not in magnitude 

(c) No change in direction of field          (d) No change in direction perpendicular to field 

39. The electric potential at the surface of an atomic nucleus (Z = 50) of radius 9.0×10-13  cm is 

(a) 80 volts         (b) 8 ×106 volts           (c) 9 volts          (d) 9 ×105 volts 

40. Two parallel plates separated by a distance of 5 mm are kept at a potential difference of  50 V. A particle  of mass 10-15 kg and charge 10-11 C enters in it with a velocity 107 m/s. The acceleration of the particle will be  

(a) 108 m/s2         (b) 5 ×105 m/s2                   (c) 105 m/s2                    (d) 2 ×103 m/s2

41. Four charges +Q, -Q, +Q, -Q are placed at the corners of a square taken in order. At the centre of the square 

42. Charges 4Q, q and Q and placed along x-axis at positions x=0, x=l/2 and x=l , respectively. Find the value of q so that force on charge Q is zero 

(a) Q                  (b) Q / 2                 (c) -Q / 2                  (d) -Q

43. The electric potential at a point on the axis of an electric dipole depends on the distance r of the point from the dipole as

44. An electric dipole consisting of two opposite charges of 2μC each separated by a distance of 3 cm is placed in an electric field of 2 ×105 N/C. The maximum torque on the dipole will be 

(a) 12 ×10-1 Nm            (b) 12 ×10-3 Nm           (c) 24 ×10-1 Nm            (d) 24 ×10-3 Nm

45. If be the electric field strength of a short dipole at a point on its axial line andthat on the equatorial line at the same distance, then

46. The electric intensity due to a dipole of length 10 cm and having a charge of 500 μC , at a point on the axis at a distance 20 cm from one of the charges in air, is

(a) 6.25 ×107  N/C           (b) 9.28 ×107   N/C           (c) 13.1 ×1011   N/C           (d) 20.5 ×107   N/C

47. The distance between H+ and Cl- ions in the HCl molecule is 1.28 Å. What will be the potential due to this dipole at a distance of 12 Å on the axis of dipole 

(a) 0.13 V           (b) 1.3 V           (c) 13 V           (d) 130 V

48. For a given surface the Gauss's law is stated as 

. From this we can conclude that 

 (a) E is necessarily zero on the surface 

 (b) E is perpendicular to the surface at every point 

 (c) The total flux through the surface is zero 

 (d) The flux is only going out of the surface

49. The S.I. unit of electric flux is  

(a) Weber       (b) Newton per coulomb         (c) Volt × metre        (d) Joule per coulomb

50. A charge q is placed at the centre of a cube. Then the flux passing through one face of the cube will be

Everyday, i will add 5 numericals to this list.