Question

A dielectric slab of thickness t is introduced between the plates of a parallel plate capacitor of area A and separation d (where t < d). Find an expression for the capacitance with the dielectric slab.

Answer 1

In the absence of a dielectric slab, the capacitance of a parallel plate capacitor is given by:

C = `(A epsilon_o)/d`

When a dielectric slab of thickness t (t < d) is introduced between the plates without touching the plates, the electric field in air:

E_o = `sigma/epsilon_o`    ...(σ is charge density given by `q/A`.)

But on account of polarisation of the dielectric, the electric field inside the dielectric changes to:

E = `E_o/K`

If the potential difference between the plates of the capacitor be V.

Now, then clearly,

V = E_o (d − t) + E_t

= `E_o(d - t) + E_o/K t`

= `E_o(d - t + t/K)`

= `sigma/epsilon_o (d - t + t/K)`

= `q/(A epsilon_o) (d - t + t/K)`