A circular coil with $200$ turns has a radius of $2\mathrm{.}0$ cm$.($a$)$ What current through the coil results in a magnetic dipole moment of $3\mathrm{.}0$ Am$2?($b$)$ What is the maximum torque that the coil will experience in a uniform field of strength $5\mathrm{.}0102$T$?($c$)$ If the angle between and B is $45,$ what is the magnitude of the torque on the coil? $($d$)$ What is the magnetic potential energy of coil for this orientation?