Four dipoles having charge $ \pm e$ are placed inside a sphere. The total flux of ${\vec E}$ coming out of the sphere is
zero
$\frac{{4e}}{{{\varepsilon _0}}}$
$\frac{{8e}}{{{\varepsilon _0}}}$
$\frac{{10e}}{{{\varepsilon _0}}}$
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
A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now........$pF$
Find capacitance across $AB$
Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the plane of equilateral triangle and passing through its centre (see figure). As a result, the first small sphere acquires charge $q_1$ and second charge $q_2 (q_2 < q_1)$ . The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$ , $l >> r$ , $d >> R$ , $d >> r$ )
If there are $n$ capacitors in parallel connected to $V \,volt$ source, then the energy stored is equal to