When two spheres having $4 Q$ and $-2 Q$ charge are placed at a certain distance,the force acting between them is $F$. Now they are connected by a conducting wire and again separated from each other. Now they are kept at a distance half of the previous one. The force acting between them is . . . . . . .

Two spheres of electric charges $+2 \ nC$ and $-8 \ nC$ are placed at a distance '$d$' apart. If they are allowed to touch each other,what is the new distance between them to get a repulsive force of the same magnitude as before?

The charge per unit length of the four quadrants of the ring are $2\lambda$,$-2\lambda$,$\lambda$,and $-\lambda$ respectively. The electric field at the centre is

$A$ unit positive point charge of mass $m$ is projected with a velocity $V$ inside a tunnel as shown. The tunnel is made inside a uniformly charged non-conducting sphere of radius $R$ and volume charge density $\rho$. The minimum velocity with which the point charge should be projected such that it can reach the opposite end of the tunnel is equal to

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 $(\beta)$.

Two charges each of magnitude $Q$ are fixed at a distance of $2a$ apart. $A$ third charge ($-q$ of mass $m$) is placed at the midpoint of the two charges. If the $-q$ charge is slightly displaced perpendicular to the line joining the charges,find its time period.