A flat square loop 20cm on a side is rotated with constant angular velocity omeg

Question

A flat square loop 20cm on a side is rotated with constant angular velocity omega = 20rad/s in a uniform magnetic field. At t = 0s the normal to the loop makes an angle 0degree with the direction of the magnetic field. Loop's resistance is 10ohm. What should be the magnitude of the magnetic field to produce maximum value of emf in the loop of 10V? Write an equation describing emf in the loop as a function of time. What is the peak value of current in the loop? What is the current through the loop at t = 0.1s?

Explanation / Answer

magnetic flux = N*B*A*cos(wt)

induced emf E= -rate of change in flux

E = N*B*A*sin(wt)*w

Emax = N*B*A*w

10 = 1*B*pi*0.2^2*20

B = 3.98 T

++++++++++++

E = N*B*A*w*sin(wt)

______________

Imax = Emax/R = 10/10 = 1A

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i = Imax*sinwt = 1*sin(20*0.1) = 0.91 A

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