The figure shows an arrangement of bar magnets in different configurations. Each bar magnet has a magnetic dipole moment m. The figure which has the maximum magnetic dipole moment _______.

configuration (C)

The correct answer is Option (3) → configuration (C)

Given:

Each bar magnet has a magnetic dipole moment $m$.

Concept:

When two magnetic dipoles of equal magnitude $m$ are placed at an angle $\theta$, the resultant magnetic dipole moment is

$M = \sqrt{m^2 + m^2 + 2m^2\cos\theta} = 2m\cos\left(\frac{\theta}{2}\right)$

Calculations:

For configuration (A): $\theta = 90^\circ \Rightarrow M = 2m\cos45^\circ = \sqrt{2}m$

For configuration (B): $\theta = 180^\circ \Rightarrow M = 2m\cos90^\circ = 0$

For configuration (C): $\theta = 30^\circ \Rightarrow M = 2m\cos15^\circ = 1.93m$

For configuration (D): $\theta = 60^\circ \Rightarrow M = 2m\cos30^\circ = 1.73m$

Hence, the maximum magnetic dipole moment is in configuration (C).