In a uniform electric field, a cube of side $1\ cm$ is placed. The total energy stored in the cube is $8.85\ μJ$ . The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is

A parallel plate capacitor of capacity ${C_0}$ is charged to a potential ${V_0}$

$(i)$ The energy stored in the capacitor when the battery is disconnected and the separation is doubled ${E_1}$

$(ii)$ The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is ${E_2}.$

Then ${E_1}/{E_2}$ value is

If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

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 $x=$________.

The insulated spheres of radii ${R_1}$ and ${R_2}$ having charges ${Q_1}$and ${Q_2}$ respectively are connected to each other. There is

If initial charge on all the capacitors were zero, work done by the battery in the circuit shown is ........... $mJ$