+5 points KatzPSE1 32.P.045 My Notes Ask Your Teacher The magnetic flux through

Question

+5 points KatzPSE1 32.P.045 My Notes Ask Your Teacher The magnetic flux through each turn of a 130-turn coil is given by = 8.25 x 10-3 sin(wt), where is the angular speed of the coil and is in webers. At one instant, the coil is observed to be rotating at a rate of 8.60 x 102 rev/min. (Assume that t is in seconds.) (a) What is the induced emf in the coil as a function of time for this angular speed? (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that is in volts. Do not include units in your answer.) (b) What is the maximum induced emf in the coil for this angular speed?

Explanation / Answer

a)

emf e = rate of change of magnetic flux

e = N*d(phi_B)/dt

e = N*(d/dt)(8.25*10^-3*sin(w*t))

e = 130*8.25*10^-3*cos(w*t)*w

w = 8.6*10^2*2*3.142/60 = 90 rad/s

e = 130*8.25*10^-3*cos(90*t)*90

e = 96.525*cos(90*t)

b) maximum induced emf is = 96.525 V

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