If the charge on a capacitor is increased by $2\, C$ the energy stored in it increases by $21\%$. The original charge on the capacitor (in coulomb) is

A wheel having mass $m$ has charges $+q $ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of uniform vertical electric field $E =$  

In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.

We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is

Figures below show regular hexagons, with charges at the vertices, In which of the following cases the electric field at the centre is not zero.

Assertion : The positive charge particle is placed in front of a spherical uncharged conductor. The number of lines of forces terminating on the sphere will be more than those emerging from it.

Reason : The surface charge density at a point on the sphere nearest to the point charge will be negative and maximum in magnitude compared to other points on the sphere

A charge $Q$ is distributed over two concentric hollow spheres or radius $r$ and $R(> r)$ such that the surface densities are equal. The potential at the common centre is