Question

Explain how does capacity of parallel plate capacitor change on introducing a conducting slab.

Answer 1

Let q = charge on the plate A.

A = area of plate.

d = distance between the plates 

When a slab of a conductor is introduced between the plates of parallel plate capacitor, a negative induced charge density develops on the upper side and a positive induced charge density on its lower side due to polarisation thereby reducing the field to zero in the interior of the slab.

The capacitance of the capacitor when there is vacuum between its two plates.

C₀ = \(\frac{\varepsilon_0A}{d}\) .........................(1)

On introducing the conducting slab the field will last long for distance (d - t) instead of d

∴ Potential difference between the capacitor plates

∴ C > C₀

i.e. the presence of a conducting slab increases the capacitance of the capacitor.

Special Case, If t = d and the conductor is kept insulated with the plates of the capacitor

From Eq. (3),

C = \(\frac{d}{d-d} C_0 = \frac{d}{0} = ∞ \)

i.e. the capacitance of the capacitor becomes infinite.