Question

The rotating loop in an AC generator is a square 13.0 cm on a side. It is rotated at 80.0 Hz in a uniform field of 0.800 T. Calculate the following quantities as functions of time t, where t is in seconds.

(a) the flux through the loop

mT·m²

(b) the emf induced in the loop

V

(c) the current induced in the loop for a loop resistance of 2.00 Ω

A

(d) the power delivered to the loop

W

(e) the torque that must be exerted to rotate the loop

mN·m

Answer 1

The area of a square = s² = 0.13²m² = 0..0169m²
Do everything in meters, not centimeters
ω = 2πf = 2π*80 = 160π = 502.4 rad/s
Area A(t) = 0.13²*sinωt
Note: I used sinωt but could have used cosωt. The starting position of the loop is not given.
Φ(t) = B*A(t) = 0.8*0.0169*sinωt = 0. 01352*sinωt<----- a)

Emf = d(BA)/dt = B*ω*0.018*cos565.5t = 5.434*cos502.4t <----- b)
Emf/R = 5.434/2.0 = 2.717amp * cos502.4t <------ c)
Power = Emf*I = Emf²/R = 14.76*cos²502.4t <----- d)
Power = Torque*ω ------> Torque = Power/ω = .433Nm <----- e)