Consider a magnetic dipole $($current carrying coil$)$with N$=250,$radius r$=9\mathrm{.}0010-3$m$,$current I$=100$A

$($a$)$Calculate its dipole moment

$($b$)$Imagine it's placed in a magnetic field B$=0\mathrm{.}856$T$.$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?