Derive the expression for the capacitance of the parallel plate capacitor.
Step 1: Given
A capacitor whose capaciatnce is to be calculated
Step 2: Formula used
Where are charge density and electrical permittivity respectively.
and Q= charge and V= potential
Step 3: Derivation of the expression for capacitance.
Place the two plates parallel to each other separated by a distance d and the cross-sectional area of each plate is A.
The electric field by a single thin plate
The electric field between the two plates
Also, the potential difference between the two plates is
⟹
Capacitance
Thus we get capacitance of parallel plate capacitor