Question

Define capacitance and give its SI units. prove that the total electostatic energy stored in a prallel plate capacitor is 1/2 CV² Hence derive the expression for the energy density of the electric field at its base.

Answer 1

Capacitance of a capacitor- Capacitance of a conductor of numerically equal to the ratio of the electric charge required to its electric potential due to that charge.

When a conductor is given some electric charge, it is raised to some potential.

Then, ∴ C = Q/V

SI unit-1 Farad (The capacitance of a conductor is said to be one farod if one coulomb of charge is sufficient to raise its potential through one volt).

Expression for the stored energy-

Suppose a parallel plate capacitor has capacitance.On plats charges are +q and -q and their potential differences is V.

∴ V = q/C ......(i)

Now dq charge is transfered than work done,

dw = vdq = q/Cdq (from (i))

Now work done in transfering total Q charge.

This work is stored in capacitor as potential energy (U).

Expression of energy density-