Question

What is electric dipole find an expression for electric potential at any point due to an electric dipole?

Answer 1

Derive an expression for electric potential at any point due to an electric dipole. Potential at point P due to the dipole along the equatorial line will be zero as P is equidistant from the two charges.

Answer 2

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