Parallel Plate Capacitor Formula

Description:

Take a parallel plate capacitor where, area  and charge carried by charge carrying plate is ‘A₁ and q’ respectively  and by supporting plate is ‘ A2 and -q’. Let the distance between the two plates of capacitor be ‘d’.  Charge density carried over both the plates be σ.

Potential difference between two plates V = E dr------(1)

In this case of parallel plate capacitor dr = d

Electric field at a point between two parallel plates carrying opposite charges :

E = σ/ε₀

Putting the value in equation (1) we get:

V = σd/ε₀

Where σ is areal charge density:

And

σ = q/A

V = qd/Aε₀

This is the value of potential difference between two plates.

We know that, C = q/v

C = qAε₀/qd

C = Aε₀/d

This is the value of capacitance in parallel plate capacitor.