The magnetic flux through each turn of a 210-turn coil is given by phi_B = 8.00

Question

The magnetic flux through each turn of a 210-turn coil is given by phi_B = 8.00 x 10^-3 sin(omegat), where omega is the angular speed of the coil and phi_B is in webers. At one instant, the coil is observed to be rotating at a rate of 8.70 x 10^2 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

here,

no of turns, n = 210
flux, fi = 8*10^-3*Sin(wt)

angular speed, w = 8.70*10^2 rev/min = 91.106 rad/s

d(fi)/dt = d/dt(8*10^-3*Sin(wt))
d' = w*Cos(wt)/125

Part A:
From Lenz's Law,
EMF = rate of change of flux
EMF = d'
EMF = w*Cos(wt)/125

Part B:
For EMF to be maximu, Cos(wt) = 0 degrees, t = 0

EMF = w/125
EMF = 91.106/125
EMF = 0.729 V

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