Question

Potential function for three dimensional doublet of strength \( \mu \) is

• A. \( \frac{\mu \cos \theta}{4\pi r^2} \)
• B. \( \frac{-\mu \cos \theta}{4\pi r^2} \)
• C. \( \frac{\mu \sin \theta}{4\pi r^2} \)
• D. \( \frac{-\mu \sin \theta}{4\pi r^2} \)

Hint:

The potential function of a doublet decreases with the square of the distance and varies with the cosine of the angle to the axis, reflecting the directional nature of dipole fields.

Answer 1

The Correct Option is A

The potential function for a three-dimensional doublet, which is a dipole with a moment \( \mu \), is given by \( \phi = \frac{\mu \cos \theta}{4\pi r^2} \). This formulation considers the radial distance \( r \) and the angle \( \theta \) to the dipole axis, following the classical potential theory in fluid dynamics.