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

Everyday, i will add 5 numericals to this list.