Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is
$2$
$3$
$4$
$6$
In an adjoining figure three capacitors $C_1,\,C_2$ and $C_3$ are joined to a battery. The correct condition will be (Symbols have their usual meanings)
A hollow conducting sphere is placed in a electric field proudced by a point charge placed at $P$ as shown in figure. Let $V_A, V_B, V_C$ be the potentials at points $A, B$ and $C$ respectively. Then
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
The work done required to put the four charges together at the corners of a square of side $a$ , as shown in the figure is
In a particle accelerator, a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m / s$. The cross-sectional area of the beam is $1.50 \,mm ^2$. The charge density in this beam (in $C / m ^3$ ) is close to