Question

Derive the expression of potential due an electric dipole at any point at distancer making an angle theta with
dipole moment. Also deduce the expression for axial and equatorial point
OR​

Answer 1

The electric dipole and expression of electric field due to electric dipole at a point is given as:----

Two equal and opposite charges separated by a small distance is called an electric dipole

Let +q and -q be the two charges separated by small distance d then dipole moment is equal to p = q.d

Electric potential at any point due to dipole:

Let a point P be r distance away from centre of dipole such that P lies at an angle Ф from axial line (line connecting two charges) as shown in figure

Also r1 and r2 are distances of point P away from charges +q and -q respectively as shown in figure.

Then potential at P due to +q is given by

. (1/∈)

Potential at P due to -q is given by

. (1/∈)

Net potential at P

V = (1/∈). [ + ]

r = - a.cosФ

r = - a.cosФ

V = (1/∈). ()[ ]

we know dipole moment here is p = q.2a

V = (1/∈). ()[ ]

So V at axial line (Ф = 0) will be

V = (1/∈). ()[ ]

and V at equatorial line (Ф = 90) will be zero