The conducting spherical shells shown in the figure are connected by a conductor. The capacitance of the system is
$4\pi {\varepsilon _0}\,\frac{{ab}}{{b - a}}$
$4\pi {\varepsilon _0}\,a$
$4\pi {\varepsilon _0}\,b$
$4\pi {\varepsilon _0}\,\frac{{{a^2}}}{{b - a}}$
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......$Vm$
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 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.
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$ , it has the same (total) energy stored in it, as the first combination has. The value of $C_2$ , in terms of $C_1$, is then
The energy stored in the capacitor is $'U'$. If an uncharged capacitor of same capacity is connected in parallel with it, then energy stored in each capacitor is