(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.

Explanation

### Step-by-Step Solution

#### (a) Definition of Electric Dipole Moment

1. **Definition**: The electric dipole moment (\( \mathbf{p} \)) is a vector quantity that represents the separation of positive and negative charges in a dipole. It is defined as:
\[ \mathbf{p} = q \cdot \mathbf{d} \]
...