Question

(a) Distinguish with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does polarised dielectric modify the original external field?
(b) A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) Charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor.
Justify your answer in each case.

Answer 1

(a)

The attached figure shows the difference in behavior of conductor and dielectric in an electric field. In dielectric, there are no free charge carriers. Aa dipole moment is induced in the molecules of the dielectric on application of external electric field. The induced opposing field is not strong enough to completely cancel the external electric field. Hence, a reduced value of electric field exists inside the material of dielectrics (unlike conductors where net electric field inside is zero).

(b)

(i) Charge stored in the capacitor will not change as it is isolated by law of conservation of charge.

(ii) Electric field inside the plates is given by:

$E=\frac{Q}{A{\epsilon }_o}$

Since charge and area of cross-section does not change, electric field is also constant.

(iii) Energy stored in capacitor is

$U=\frac{Q^2}{2C}=\frac{Q^{2}d}{2{\epsilon }_{o}A}$

Since $d$ is doubled, stored energy is also doubled. Not that energy stored is provided by the external work done to increase the distance between the plates.