Consider a magnetic dipole $($current carrying coil$)$ with $N=250,$ radius $r=9\mathrm{.}00{10}^{-3}m,$ current $I=100A$

$($a$)$ Calculate its dipole moment $$

$($b$)$ Imagine it's placed in a magnetic field $B=0\mathrm{.}856T.$ The magnetic field points along the $+z$ axis. The dipole moment vec$()$ points along the $+x$ axis. What is the magnitude of the torque it experiences?

$($c$)$ If it's held in place, what is the its potential energy $U?$

$($d$)$ Suppose we want to rotate it from vec$()$ pointing along the $+x$ axis to along the minus $z$ axis, how much work is required?