E & M Qual Problems

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