Question

An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between the, parallel to the plates and not touching either plate

Answer 1

Answer:

$C' = \frac{A\epsilon_{o}}{d - a}$

Solution:

As per the question:

Area of the plates is given by 'A'

Separation distance between the plates is 'd'

Now, after insertion of the metal plate with same area 'A' and thickness, a < d

in between the plates, the capacitance of the capacitor changes.

The capacitance of the air capacitor (parallel plate) is generally given by:

$C = \frac{A\epsilon_{o}}{d}$

where

C = Capacitor's capacitance

$\epsilon_{o}$ = Permittivity of the free space

Now, when the metal slab is inserted the distance is reduced to (d - a)

Thus

$C' = \frac{1}{2}(\frac{A\epsilon_{o}}{\frac{d - a}{2}})$

$C' = \frac{A\epsilon_{o}}{d - a}$