A thin bar magnet of magnetic moment $$M$$ is bent to form an arc of a circle making an angle $$\theta$$ (radians). Find its new magnetic moment.

PLACEHOLDER ANSWER - the answer is an expression. If the magnet has length $$L$$ and pole strength $$m$$, then $$M = mL$$. Bent into an arc of angle $$\theta$$, its radius is $$R = \frac{L}{\theta}$$ and the straight distance between its poles is the chord $$2R\sin\frac{\theta}{2} = \frac{2L}{\theta}\sin\frac{\theta}{2}$$. The new moment is $$M' = m \times \frac{2L}{\theta}\sin\frac{\theta}{2} = \frac{2M}{\theta}\sin\frac{\theta}{2}$$.