$A$ battery is used to charge a parallel plate capacitor until the potential difference between the plates becomes equal to the e.m.f. of the battery. The ratio of the energy stored in the capacitor to the work done by the battery will be

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.

$A$ piece of cloud having an area of $25 \times 10^6 \, m^2$ and an electric potential of $10^5 \, V$. If the height of the cloud is $0.75 \, km$,then the energy of the electric field between the earth and the cloud will be.....$J$

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

The capacity of a capacitor is $4 \times 10^{-6} \, F$ and its potential is $100 \, V$. The energy released on discharging it fully will be ....... $J$.

The energy stored in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $4\,\mu C$ charge,its radius will be.......$mm$. [Take: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$]