Question

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor. 

Answer 1

Capacitance of a capacitor partially filled with a dielectric

C = ε₀A/(d-t + t + t/k)

⇒ C = ε₀A/(d- d/2 +d/2k) 

= 2ε₀AK/d(K +1).