A small permanent magnet is placed in a uniform magnetic field of magnitude 0.35 T.If the maximum torque experienced by the magnet is 0.50 N · m,what is the magnitude of the magnetic moment of the magnet?

Question

Quizplus · Accepted Answer

The maximum torque ($\tau$) experienced by a magnet in a uniform magnetic field is given by the equation $\tau = \mu B \sin(\theta)$, where $\mu$ is the magnetic moment of the magnet, $B$ is the magnetic field strength, and $\theta$ is the angle between the magnetic moment and the magnetic field. The maximum torque occurs when $\sin(\theta) = 1$ (i.e., $\theta = 90^\circ$). Therefore, the equation simplifies to $\tau = \mu B$. Rearranging for $\mu$, we get $\mu = \tau / B$. Substituting the given values, $\mu = 0.50 \, \text{N} \cdot \text{m} / 0.35 \, \text{T} = 1.43 \, \text{A} \cdot \text{m}^2$, which rounds to 1.4 A·m^2, making option A correct.

A Small Permanent Magnet Is Placed in a Uniform Magnetic