If the radius of each of the plates is increased by a factor of √2 and their distance of separation decreased to
half of its initial value, calculate the ratio of the capacitance in the two cases.
Suggest any one possible method by which the capacitance in the second case be increased by n times.
10. Obtain the expression for the energy stored in a parallel plate capacitor.
In the given figure, the energy stored in C4 is 27 J. Calculate the total energy stored in
the system.
11. State the theorem which relates to enclosed charge, inside a closed surface, with the electric flux through
it. Use this to obtain the electric field due to a uniformly charged thin spherical shell at an (a) inside point;
(b) outside point.
An electric charge of 8.85 x 10-13 C is placed at the centre of a sphere of radius 1m.
What is the total electric field linked with the sphere? How will the electric flux
change if an equal and opposite charge is introduced at a distance of (a)0.5m from the
centre ; (b)1.5m from the centre.
12. (a) Electric charge is distributed uniformly on the surface of a spherical rubber balloon. Show how will
the value of electric field intensity and potential vary
a. on the surface
b. inside
c. outside?
(b)Derive an expression for energy stored in a parallel plate capacitor.
13. (a) State Gauss’s Law of electrostatics.
(b) Using Gauss’s Law find the value of electric field intensity at a point due to
infinite plane sheet of charge.
(c) If Coulomb’s Law involved
1 dependence instead of 1 would Gauss’s Law
still be true ? Give reason.
r3
r2
14. Give the principle of working of a Van de Graff generator. With the help of a labeled diagram, describe
its construction and working. How is the leakage of charge minimized from the generator?
15. Obtain the expression for the capacitance of a parallel plate capacitor.
Three capacitors of capacitances C1, C2 and C3 are connected
(i)in series,
(ii)in parallel.
Show that the energy stored in the series combination is the same as that in the
parallel combination.
16. (a) Define an electric dipole moment. Find the expression for electric field intensity at distance r due to an
electric dipole on its axial line.
(b)What happens when an electric dipole is held in a non-uniform electric field?
17. (a) When two charged conductors having different capacitances and different potentials are joined
together, show that there is always loss of energy.
(b) Three capacitors each of capacitance 9μF are connected in series. Find
(i) Equivalent capacitance of combination
(ii) Potential difference across each capacitor if the combination is connected
to a 120V supply.
18. (a) Derive an expression for the energy of a parallel plate capacitor.
(b) A 4μF capacitor is connected to another 8μf capacitor in parallel. The combination is connected across
300V. Calculate
(i) Total charge on the combination
(ii) Total energy stored in the combination.
19. What is a capacitor? Derive the expression for the capacitance of a parallel plate capacitor. By what factor
does the capacity of a metal sphere increase if its volume is tripled?