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 

In the circuit shown, a potential difference of $30\, V$ is applied across $AB$ . The potential difference between the points $M$ and $N$ is....$V$

If an insulated non-conducting sphere of radius $R$ has charge density $\rho .$ The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

A network of four capacitors of capacity equal to $C_1 = C,$ $C_2 = 2C,$ $C_3 = 3C$ and $C_4 = 4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is

Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$