Electric field strength due to a point dipole at a distance ‘r’ from it on its axial line is $\overrightarrow{E}$. Electric field strength on its equatorial line at the same distance ‘r’ will be

The electric field strength $�$E due to a point dipole at a distance $�$r along its axial line can be calculated using the formula:

$E=\frac{kp}{r^3}$​

Where:

• k is the electrostatic constant (or Coulomb's constant).
• p is the magnitude of the dipole moment.

On the equatorial line of the dipole at the same distance $�$r, the electric field strength will be different. For a point dipole, the electric field on the equatorial line is generally weaker than on the axial line.

The electric field on the equatorial line can be calculated using the formula:

$E_{\text{equatorial}}=\frac{kp}{r^3}\cdot \frac{1}{\sqrt{2}}$

This expression arises from vector addition of the electric fields produced by the two opposite charges of the dipole. The factor $\frac{1}{\sqrt{2}}$2​1​ comes from the geometry of the equatorial line, where the contributions from the positive and negative charges are perpendicular to the line joining them.

So, electric field strength on the equatorial line at the same distance 'r' will be $\frac{E}{\sqrt{2}}$