If there are $n$ capacitors in parallel connected to $V \,volt$ source, then the energy stored is equal to

Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is

An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then, the equivalent capacitance between $A$ and $B$ is .......... $\mu F$

Three charges $4q,\,Q$ and $q$ are in a straight line in the position of $0$, $l/2$ and $l$ respectively. The resultant force on $q$ will be zero, if $Q = $

In the figure a capacitor is filled with dielectric. The resultant capacitance 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