Derive an expression for the electric field intensity at a point on the equatorial line of an electric dipole of dipole moment p and length 2a. What is the direction of this field?

Question

Philoid · Accepted Answer

Let’s consider a dipole arrangement with charges, -q and +q separated by a distance AB=2a.

Hence, the dipole moment is, p=q(2a).

O is the midpoint of AB. Let OP=r.

Therefore,

Similarly,

Now, electric field at point P due to -q is

And, electric field at point P due to +q Is

Both E_+q and E_-q have two components, one parallel to AB and other Perpendicular to AB. The perpendicular components are equal in magnitude and opposite in direction, hence they cancel out.

The parallel components are given by E_-q cos