Bar Magnet: Practice Problem & Solution
A bar magnet of magnetic moment \(\vec{M}\) is placed in a uniform magnetic field \(\vec{B}\) such that \(\vec{M}\) and \(\vec{B}\) are antiparallel. If the magnet is rotated through \(90^\circ\), then the work done on the magnet will be
Solution Explained:
To solve this problem, we apply the core principles of Bar Magnet. Understanding the underlying formula is key to arriving at the correct answer below:
Work done in rotating a magnetic dipole is \(W = MB(\cos \theta_1 - \cos \theta_2)\). Since initially \(\theta_1 = 180^\circ\) and finally \(\theta_2 = 90^\circ\), \(W = MB(\cos 180^\circ - \cos 90^\circ) = MB(-1 - 0) = -MB\).
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