Five balls numbered $1$ to $5$ are suspended using separate threads. Pairs $(1,2), (2,4)$ and $(4,1)$ show electrostatic attraction while pairs $(2,3)$ and $(4,5)$ show repulsion. Therefore ball $1$ must be

A point charge $'q'$ is placed at a point inside a hollow conducting sphere. Which of the  following electric force pattern is correct ?

Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are separated by  a distance of $5\, cm$ and are uniformly charged. If the spheres are connected by a  conducting wire then in equilibrium condition, the ratio of the magnitude of the electric  fields at the surfaces of spheres $A$ and $B$ is-

Four charges are placed at the circumference of a dial clock as shown in figure. If the clock has only hour hand, then the resultant force on a charge $q_0$ placed at the centre, points in the direction which shows the time as:

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