Question

The electrostatic potential due to an electric dipole at a distance $r$ varies as:

• A. $\frac{1}{r}$
• B. $\frac{1}{r^3}$
• C. $\frac{1}{r^2}$
• D. $r$

Answer 1

Answer: (C)

$\frac{1}{r^2}$

Answer 2

The electrostatic potential V at a point along the axial line of an electric dipole (aligned along the x -axis) is given by:

$V = \frac{kp \cos \theta}{r^2}$

where: k is Coulomb's constant, p is the dipole moment ($p = q \times d$, where q is the charge and d is the separation distance), r is the distance from the dipole to the point where the potential is being calculated, and θ is the angle between the dipole axis and the line connecting the dipole to the point.

Since the potential V is inversely proportional to r 2, we conclude that the electrostatic potential due to a dipole varies as:

$V \propto \frac{1}{r^2}$