Question #43264

A small magnetic compass needle of magnetic moment $M = 0.01 \text{ A m}^2$ and moment of inertia $I = 2.0 \times 10^{-6} \text{ kg m}^2$ is suspended in a uniform magnetic field of magnitude $B$. The needle undergoes angular simple harmonic motion in a plane parallel to the magnetic field. The oscillations are observed through a telescope with an objective lens of diameter $D = 1.22 \text{ cm}$ using light of wavelength $\lambda = 600 \text{ nm}$. The amplitude of oscillation $\theta_0$ is such that the extreme position of the needle is just resolvable from its mean equilibrium position according to the Rayleigh criterion. If the maximum angular speed of the needle during the oscillation is $\Omega_{max} = 3.0 \times 10^{-3} \text{ rad s}^{-1}$, what is the magnitude of the magnetic field $B$?