Electric field inside a uniformly charged sphere of radius $R,$ is ($r$ is distance from centre, $r < R$)
$\frac{KQr}{R^3}$
$\frac{KQ}{R^2}$
$\frac{KQr^2}{R^3}$
$\frac{2KQ}{R^2}$
A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the electrical force on $Q$ is zero, then $Q/q$ equals
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.
Heat flow | Electrostatics |
$T( r )$ | $V( r )$ |
$j ( r )$ | $E ( r )$ |
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
The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$, then
Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is
Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is