A. Derive the expression for electric field at a point on the equatorial line of an electric dipole.

B. Depict the orientation of the dipole in (i) stable, (ii) unstable equilibrium in a uniform electric field.

A) The point P on the equatorial line is considered,

So, the magnitude electric field at P due to +q is,

And that due to -q is,

The net electric field is,

As shown in the diagram, where is the unit vector along the dipole axis (from -q to +q),

Hence,

For large distances (r >> a), the above equation reduces to,

Also, we know that,

Thus, finally the electric field on the equatorial line of the dipole is,

B) When a dipole is placed in uniform external electric field, it is stable when it is parallel ( = 0) to the electric field and unstable when it is anti-parallel ( = 180) to the electric field as shown,