Energy per unit volume for a capacitor having area $A$ and separation $d$ kept at potential difference $V$ is given by

The plates of a parallel plate capacitor have an area of $90 \,cm ^{2}$ each and are separated by $2.5\; mm .$ The capacitor is charged by connecting it to a $400\; V$ supply.

$(a)$ How much electrostatic energy is stored by the capacitor?

$(b)$ View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume $u$. Hence arrive at a relation between $u$ and the magnitude of electric field $E$ between the plates.

A parallel plate capacitor has an electric field of ${10^5}\,V/m$ between the plates. If the charge on the capacitor plate is $1\,\mu \,C$, the force on each capacitor plate is……$N$

A $16\  \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\  \Omega$ is connected across one of its sides. If a $4\  \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.

A condenser having a capacity $2.0$ micro farad is charged to $200\;volts$ and then the plates of the capacitor are connected to a resistance wire. The heat produced in joules will be