The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is

Consider the situation shown. The switch $S$ is opened for a long time and then closed. The charge flown through the battery when $S$ is closed

 An insulator plate is passed between the plates of a capacitor. The the displacement current

A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R$ $( R > r ) .$ If the surface charge densities on the two shells are equal, the electric potential at the common centre is

If $\vec E = \frac{{{E_0}x}}{a}\hat i\,\left( {x - mt} \right)$ then flux through the shaded area of a cube is

A hollow conducting sphere is placed in a electric field proudced by a point charge placed at $P$ as shown in figure. Let $V_A, V_B, V_C$ be the potentials at points $A, B$ and $C$ respectively. Then