A charge $Q$ is divided into two parts of $q$ and $Q - q$. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

Two masses $M_1$ and $M_2$ carry positive charges $Q_1$ and $Q_2$, respectively. They are dropped to the floor in a laboratory set up from the same height, where there is a constant electric field vertically upwards. $M_1$ hits the floor before $M_2$. Then,

In a certain region of space, there exists a uniform electric field of value $2\times10^2\hat k\, Vm^{-1}$. A rectangular coil of dimension $10\, cm\times20\, cm$ is placed in the $xy$ plane. The electric flux through the coil is......$Vm$

The equivalent capacitance of the combinatio shown in Figure is

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 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