The equivalent capacitance between points $A$ and $B$ of the circuit shown will be

Consider a cube of uniform charge density $\rho$. The ratio of electrostatic potential at the centre of the cube to that at one of the corners of the cube is

In the given circuit if point $C$ is connected to the earth and a potential of $+2000\,V$ is given to the point $A$ , the potential of $B$ is.....$V$

The electric potential $V$ at any point $O$ ($x, y, z$ all in metre) in space is given by $V=4x^2\, volt$. The electric field at the point $(1\,m, 0, 2\,m)$ in $volt/meter$ is

A network of four capacitors of capacity equal to $C_1 = C,$ $C_2 = 2C,$ $C_3 = 3C$ and $C_4 = 4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is

A thin spherical conducting shell of radius $R$ has charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is