A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$

A charged particle $'q'$ is shot from a large distance with speed $v$ towards a fixed  charged particle $Q$. It apporaches $Q$ upto a closet distance $r$ and then returns. If $q$ were given a speed $'2v$', the closest distance of approach would be 

Five indentical capacitor plates, each of area $A,$ are arranged such that adjacent plates are at distance $d$ apart. The plates are connected to a source of $emf$ $V$ as shown in fig. Then the charges $1$ and $4$ are, respectively :-

The potential $V$ is varying with $x$ and $y$ as $V = \frac{1}{2}({y^2} - 4x)\,volts$ The field at $(1\,m,\,1\,m)$ is

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$ , the energy stored in the capacitor is

$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric radius $a$ , outer radius $b$ and dielectric constant $k$ . If sphere $A$ be given a charges $Q$ , the potential at the outer surface of the dielectric is