Well, In this article, we are going to derive the expression for the capacitance of a parallel plate capacitor when a dielectric slab of thickness t is inserted between the plates. Wants to know all about the derivation, stay tuned with us till the end…
DERIVATION FOR THE CAPACITANCE
Let’s take a parallel plate capacitor having a plate surface area is A. A dielectric slab of thickness t is inserted between the plates. And the dielectric slab has the dielectric constant K and the permittivity of its medium is ε. See the figure below :
After putting the dielectric slab of thickness t the remaining distance will be (d – t). Let the electric field inside the dielectric slab is E and the field inside the plates and outside the slab is $E_0$.
The electric field inside the slab is given as-
And the electric field outside the slab is given as –
The total potential difference between the plates is given as the sum of the potential difference due to the slab and without the slab. Which is clearly written below :
Capacitance of any capacitor is given as charge per unit potential difference. Let’s put the value of potential difference in the formula of capacitance.
This is the required value of capacitance of a parallel plate capacitor when a dielectric slab of thickness t is inserted between the plates.