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

`C' = (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 = (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' = (1)/(2)((A\epsilon_(o))/((d - a)/(2)))`

`C' = (A\epsilon_(o))/(d - a)`