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In a medium of dielectric constant $K$, the electric field is $\vec E$ . If ${ \varepsilon _0}$ is permittivity of the free space, the electric displacement vector is
Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be
Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $ - V$. These are then connected by means of a fine wire. The loss of energy will be
A $10\,\mu F$ capacitor is charged to a potential difference of $1000\, V$. The terminals of the charged capacitor are disconnected from the power supply and connected to the terminals of an uncharged $6\, \mu F$ capacitor. What is the final potential difference across each capacitor?......$V$
Two metal spheres, one of radus $R$ and the other of radius $2 R$ respectively have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?
In an isolated parallel plate capacitor of capacitance $C$, the four surface have charges ${Q_1}$, ${Q_2}$, ${Q_3}$ and ${Q_4}$ as shown. The potential difference between the plates is