Why is an insulator sometimes called a dielectric? What is the main difference between free and bound charge? Generally one of the two plates of a capacitor system is earthed, why? Derive the expression for the energy stored in a charged capacitor.

Explanation

Insulators can polarise to produce dipole moment or an equal and oppositely charge surfaces, hence they are called dielectrics.
■ Free charge can be transferred from one body to another, but bound charged cannot be transferred.
■ To conduct the expelled charge during induction (occurred during charging) one of plates of capacitor is earthed.
Energy stored in a capacitor
The energy of a charged capacitor is measured by the total work done in charging the capacitor to a given potential. Let. us assume that initially both the plates are uncharged. Now, we have to repeatedly move small positive charges from one plate and transfer them to the other plate.
Now, when an additional small charge (do,) is transferred from one plate to another plate, the small work done is given by
`dW = Vdq = q^(.)/C dq` [`therefore` charge on plate when dq charge is transferred beg q.]
The total work done in transferring charge Q is given by
`W = int_(0)^(Q) q^(.)/C dq = 1/2int_(0)^(Q) q. dq`
`=1/C [(q^(.))^(2)/2]_(0)^(Q) = Q^(2)/(2C)`
This work is stored as electrostatic potential energy U in the capacitor.
`U = Q^(2)/(2C)`
`= (CV)^(2)/(2C) = 1/2CV^(2) [therefore Q = CV]`