A magnetic molecule is placed along the axis of a circular conductor of radius \(a\) at a point where any radius of the circle subtends an angle \(\alpha\). The magnetic moment of the molecule is periodic and equal to \(\mu\cos pt\). Shew that the periodic current in the conductor is \[ \frac{2\pi\mu p\sin^3\alpha}{a} \frac{pL\cos pt - R\sin pt}{p^2L^2+R^2}. \] Find the mechanical force on the conductor at any time, and prove that its mean value is \[ \frac{6\pi^2\cos\alpha\sin^4\alpha}{a^3} \frac{\mu^2 p^2 L}{p^2L^2+R^2}; \] where \(L,R\) are the coefficient of self-induction and resistance of the conductor.