E & M Qual Problems

1.) A rigid, infinitesimally thin conducting ring of radius [math]a=0.15 m[/math] and mass [math]m=1.0kg[/math] is initially oriented nearly vertically in a uniform vertical magnetic field [math]\vec{B} = B_0 \hat{z}[/math] where [math]B_o = 2.5 Telsa[/math]. The resistance of the ring is [math]R = 10^{-3} \Omega[/math]. The ring is initially at rest at a polar angle of [math]\theta_0 = 1.0 mrad[/math] with respect to the [math]\hat{z}[/math]-axis. The orientation of the rin is such that the unit normal vector [math]\hat{n}[/math] lies in the [math]\hat{y} -\hat{z}[/math] plane, initially nearly parallel to the [math]-\hat{y}[/math] direction.

If the ring is allowed to fall with no slipping under the influence of the earth's gravitational field, the presence of the magnetic field acts as a magnetic "brake", slowing the fall of the ring by a considerable amount, as if the ring was falling in a highly viscous fluid.

a.) Calculate the instantaneous EMP [math]\epsilon(t)[/math] induced in the ring in terms of the polar angle [math]\theta[/math] and the angular velocity [math]\dot{\theta}[/math]