Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x-$ axis at which the net electric field due to these two point charges is zero is

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges in  them repel each other with a force $F$ when kept apart at some some distance. $A$ third  spherical conductor having same radius as that of $B$ but uncharged, is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both.  The new force of repulsion between $B$ and $C$ is-

A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R$ $( R > r ) .$ If the surface charge densities on the two shells are equal, the electric potential at the common centre is

A parallel plate capacitor has plates with area $A$ and separation $d$. A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d$ is introduced. The ratio of energy stored in the capacitor before and after slab is introduced, is

The value of electric potential at any point due to any electric dipole is

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+ q$ and $-q$. The potential difference between the centres of the two rings is