Two condensers, one of capacity $C$ and the other of capacity $\frac{C}{2}$ , are connected to a $V\, volt$ battery, as shown. The work done in charging fully both the condensers is
$\frac{1}{2}CV^2$
$2CV^2$
$\frac{1}{4}CV^2$
$\frac{3}{4}CV^2$
A thin square plate is placed in $x-y$ plane as shown in fig. such that is centre coinsides with origine it's charge density at point $(x, y)$ is $\sigma = \sigma _0xy$ (where $\sigma _0$ is constant). Find total charge on the plate.
Four dipoles having charge $ \pm e$ are placed inside a sphere. The total flux of ${\vec E}$ coming out of the sphere is
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
As shown in the fig. charges $+\,q$ and $-\,q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is
The equivalent capacitance between points $A$ and $B$ of the circuit shown will be