The next three questions refer to this situation: A thin square coil has 79 turn

Question

The next three questions refer to this situation: A thin square coil has 79 turns of conducting wire. It is rotating with constant angular velocity in a uniform magnetic field B of 0.390T. At times there is NO magnetic flux through the coil, and at other times, there is the maximum possible flux. The graph below shows the magnetic flux PHI through ONE turn of the coil as a function of time.

A.What is the length of a side of the coil?

B.Calculate the angular velocity of the coil. Use units of rad/s.

C. Evaluate the magnitude of the induced voltage in the coil, Vemf, at time t= 2.60 s.

Explanation / Answer

The preak EMF per turn is EMF = 170 / 680 = 0.25 Using Faraday's Law EMF = - d(magnetic flux)/dt = -d ( B A(t) ) / dt EMF = - B dA(t)/dt where A is the cross sectional area given by A(t) = L^2 sin(wt) where w = 90rads/sec. Then, the EMF is EMF = - B L^2 w cos(wt) Now we use the peak EMF per turn and solve for L when cos(wt)=1. This is 0.25 = - (0.29)L^2 thus L = sqrt (0.25/0.29) = 0.92 m. flux = phi = BA cos wt A = area of crossection = 0.018*0.018 m^2 w = angular speed, t =time instantaneous emf = e(t) = - N d(phi)/dt = - w (BA) [- sin wt] e (max) = e0, when sin wt = 1 or angle wt = 90 degree ---------------------- eo = BANw w = e0/BAN = 3*10^-3/(0.805*0.018*0.018*190) w = 0.0605 rad/sec e=-?f/?t Considering that vectors B and S are in the same direction, f = n B S =200* 0.0256* 1.4= 7.168Wb e=-7.168/2.5= - 2.8672V If you considered that vectors B and S are in opposite directions, you would have had e=2.8672 circulating in an opposite manner; Meaning= same thing!

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