$A$ pendulum bob of mass $30.7 \times 10^{-6} \, kg$ and carrying a charge $2 \times 10^{-8} \, C$ is at rest in a horizontal uniform electric field of $20000 \, V/m$. The tension in the thread of the pendulum is $(g = 9.8 \, m/s^2)$.

Two identical metallic spheres $A$ and $B$ when placed at a certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at the midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be:

Charges are placed on the vertices of a square as shown. Let $\vec E$ be the electric field and $V$ be the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then

Six point charges are placed at the vertices of a regular hexagon as shown in the figure. Three of the charges are $+q$ and the other three are $-q$. Starting from $P$ and moving clockwise,the electric field at the center $O$ is twice the electric field due to a single charge $+q$ at $R$. Which of the following arrangements of charges at $P, Q, R, S, T, U$ is correct?

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

$A$ solid sphere of radius $R$ carries a charge $(Q+q)$ distributed uniformly over its volume. $A$ very small point-like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$. If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure),then: (assume the remaining portion to be spherical).