A circular coil with area A and N turns is free to rotate about a diameter that coincides with the x-axis. Current I is circulating in the coil. There is a uniform magnetic field `vec B` in the the positive y direction. Calculate the magnitude and direction of the torque `vec tau` and the value of the potential energy U, when the coil is oriented as shown in parts (a) through (d) of Fig. 1.79.

Explanation

(a) `phi=90^@: tau=NIAB sin(90^@)=NIAB`
Direction: `hatkxxhatj=-hati, U=-MBcos phi=0`
(b) `phi=0^@: tau=NIAB sin(0)=0` no direction,
`M=NIA, U=-MBcosphi=-NIAB`
(c) `phi=90^@: tau=NIAB sin(90^@)=NIAB`
Direction: `-hatkxxhatj=-hati, U=-MBcos phi=0`
(d) `phi=180^@: tau=NIAB sin(180^@)=0` no direction,
`U=-MBcosphi=-NIAB`