Two point charges of $ + 2\,\mu C$ and $ + 6\,\mu C$ repel each other with a force of $12\, N$. If each is given an additional charge of $ - 4\,\mu C$, then force will become

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

The potential $V$ is varying with $x$ and $y$ as $V = \frac{1}{2}({y^2} - 4x)\,volts$ The field at $(1\,m,\,1\,m)$ is

If an insulated non-conducting sphere of radius $R$ has charge density $\rho .$ The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

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

A hollow metal sphere of radius $5\, cm$ is charged so that the potential on its surface is $10\, V$. The potential at the centre of the sphere is.....$V$