(a)A pair of two charges equal in magnitude and opposite in signs separated by a very small distance is known as an electric dipole.
For equipotential surfaces where E is increasing uniformly d should decrease uniformly that's why the equipotential surfaces are compactly arranged closer to the charges and we can see that the electric field lines are always perpendicular to the equipotential surface.
we know that the electric field is given by,
From the figure, we can see that the sine components get mutually cancelled and the cosine components can be added.
Now we get,
Since magnitudes are same,
Substituting the values in equation 1 we get,
Now dipole moment =2qa
So, a can be eliminated in the denominator.
This is the required equation and the direction of the electric field will be opposite to the direction of the electric dipole.
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