I need help with this question please The rotor in a certain

I need help with this question please!!

The rotor in a certain electric motor is a flat, rectangular coil with 76 turns of wire and dimensions 2.50 cm by 4.00 cm. The rotor rotates in a uniform magnetic field of 0.800 T. When the plane of the rotor is perpendicular to the direction of the magnetic field, it carries a current of 6.4 mA. In this orientation, the magnetic moment of the rotor is directed opposite the magnetic field. The rotor then turns through one-half revolution. This process is repeated to cause the rotor to turn steadily at 3600 rev/min. Find the maximum torque acting on the rotor Find the peak power output of the motor. Determine the amount of work performed by the magnetic field on the rotor in every full revolution. Your response is off by a multiple of ten. J What is the average power of the motor? Your response is off by a multiple of ten. W

Solution

here,

1 rev/min = 0.10472 rad/s

no of turns, n = 76 turns

Area of coil, A = L * B = 2.50 * 4 cm = 10 cm^2 = 0.001 m^2

magnatic field, B = 0.8 T

Current in Coil, I = 6.4 mA = 0.0064 A

Angular rspeed of rotor, w = 3600 rev/min = 377 rad/s

Part A:
Maximum Torque, t = n*I*A*B*Sin90 ( 90 degrees for maximum torque)
t = 76 * 0.0064*0.001*0.8*Sin90
t = 0.00038912 N.m

Part B:
POwer, P = torque * w = 0.00038912 * 377 = 0.1467 Watts

Part C:
The work done is the (negative of the) change in the potential energy, so that gives the answer for half of a revolution. Doubling that gives the coefficient of 4 for the full revolution.

so, Work done = 4 * n * I * A = 4 * 90 * 0.0064 * 0.001 = 0.002304 J

Part D:
Average power, P = Work done /time = 0.002304 / (60/3600) = 0.13824 Watts