(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Electric dipole moment is the product of either charges or the distance between two equal and opposite charges.

It is a vector quantity.

Electric dipole moment at a point on the equatorial plane:

Consider a point P on broad side on the position of dipole formed of charges + q and - q at separation 2l. The distance of point P from mid-point O of electric dipole is r. 

 

Let E₁ and E₂ be the electric field strength due to charges +q and –q of electric dipole.

From the fig. we have

 
Now, in order to find the resultant electric field, we resolve the components along and perpendicular to AB.

The components perpendicular to AB are sin components and they being equal and opposite to each other cancel each other.

Therefore,

Resultant electric field is given by, 

E₁ = E₁cos θ + E₂ cos θ

But, 

 

From the fig. we can see that,

  

If dipole is infinitesimal and point P is far away, then l² can be neglected as compared to r².

Therefore, 

 

b) Equipotential surfaces due to an electric dipole is given by,  
                               

Electric potential is zero at all points in the plane passing through the dipole equator.