$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

Four identical point masses, each of mass $m$ and carrying charge $+q$, are placed at the corners of a square of side $a$ on a frictionless horizontal surface. If the particles are released simultaneously, the kinetic energy of the system when they are infinitely far apart is

$A$ cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be

$A$ charge $+q$ is situated at a distance $d$ away from both the sides of a grounded conducting $L$-shaped sheet as shown in the figure. The force acting on the charge $+q$ is:

For a thin spherical shell of radius $R$ with a uniform surface charge density, which of the following graphs best represents the variation of the electric field magnitude $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the center?

Two fixed,identical conducting plates $(\alpha)$ and $(\beta)$,each of surface area $S$,are charged to $-Q$ and $q$,respectively,where $Q > q > 0$. $A$ third identical plate $(\gamma)$,free to move,is located on the other side of the plate with charge $q$ at a distance $d$ as per the figure. The third plate is released and collides with the plate $(\beta)$. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $(\beta)$ and $(\gamma)$.
$(a)$ Find the electric field acting on the plate $(\gamma)$ before collision.
$(b)$ Find the charges on $(\beta)$ and $(\gamma)$ after the collision.
$(c)$ Find the velocity of the plate $(\gamma)$ after the collision and at a distance $d$ from the plate $(\beta)$.