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?

Draw the field lines for a bar magnet,a current-carrying finite solenoid,and an electric dipole.

$A$ 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 tiny spheres carrying charges $1.5 \; \mu C$ and $2.5 \; \mu C$ are located $30 \; cm$ apart. Find the potential and electric field:
$(a)$ at the mid-point of the line joining the two charges,and
$(b)$ at a point $10 \; cm$ from this midpoint in a plane normal to the line and passing through the mid-point.

$A$ 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).

Two equal negative charges $-q$ each are fixed at the points $(0, a)$ and $(0, -a)$ on the $Y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $X$-axis. The charge $Q$ will :-