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 _______.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → configuration (C)
The magnetic dipole moment of a bar magnet is a vector pointing from its S pole to its N pole, and the moments of the two magnets add as vectors. For two equal moments \( m \) with angle \( \alpha \) between them,
\( \displaystyle m_{\mathrm{net}} = 2m\cos\frac{\alpha}{2} \)
The angles between the S-to-N directions, read from the figure:
\( (A)\ \alpha = 90^\circ: \quad m_{\mathrm{net}} = 2m\cos 45^\circ \approx 1.41\,m \)
\( (B)\ \alpha = 180^\circ: \quad m_{\mathrm{net}} = 0 \)
\( (C)\ \alpha = 30^\circ: \quad m_{\mathrm{net}} = 2m\cos 15^\circ \approx 1.93\,m \)
\( (D)\ \alpha = 60^\circ: \quad m_{\mathrm{net}} = 2m\cos 30^\circ \approx 1.73\,m \)
The smallest angle between the moments gives the largest resultant, so configuration (C) has the maximum dipole moment.