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 point charge $q$ is situated at a distance $d$ from one end of a thin non - conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length) as shown in fig.Then the magnitude of electric force between them is
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
Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then
Consider a system of there charges $\frac{q}{3},\,\frac{q}{3}$ and $-\frac{2q}{3}$ placed at point $A, B$ and $C,$ respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and $\angle CAB\, = \,{60^o}$
A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to