1) 2) 3) 4) 5) 6) A conducting wire formed in the shape of a right triangle with

Question

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A conducting wire formed in the shape of a right triangle with base b = 31 cm and height h = 62 cm and having resistance R = 2.7 ?, rotates uniformly around the y-axis in the direction indicated by the arrow (clockwise as viewed from above (looking down in the negative y-direction)). The triangle makes one complete rotation in time t = T = 1 seconds. A constant magnetic field B = 1.4 T pointing in the positive z-direction (out of the screen) exists in the region where the wire is rotating. What is ?, the angular frequency of rotation? What is Imax, the magnitude of the maximum induced current in the loop? At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux ?1 at time t = t1 = 0.375 s? What is I1, the induced current in the loop at time t = 0.375 s? I1 is defined to be positive if it flows in the negative y-direction in the segment of length h.Which of the folowing statements about ?o, the magnitude of the flux through the loop at time t = to = 0.25 s, and Io, the magnitude of the current through the loop at time t = to = 0.25 s, is true? ?max and Imax are defined to be the maximum values these quantites achieve during the complete rotation.?o = 0 and Io = 0?o = 0 and Io = Imax?o = ?max and Io = 0?o = ?max and Io = Imax Suppose the frequency of rotation is now doubled. How do ?max, the maximum value of the flux through the loop, and Imax, the maximum value of the induced current in the loop change??max and Imax both double?max doubles and Imax remains the same?max remains the same and Imax doubles Both ?max and Imax remain the same

Explanation / Answer

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1) w = 2*pi/T = 5.23 rad/s
2)
N = 1
A = 0.5*0.28*0.83 = 0.1162 m^2
B = 1.1 T
w = 5.23 rad/s
induced emf = N*B*A*w = 1*1.1*0.1162*5.23 = 0.6685 volts
induced current = induced emf/R = 0.6685/2.8 = 0.2387 A

3) let theta1 = 0 is the angle between normal and B at at t = 0
let theta2 is the angle between normal and B at t = 0.45 s
w = (theta2 - theta1)/(t2-t1)
5.23 = (theta2 - 0)/(0.45 - 0)
theta2 = 5.23*0.45 = 2.3535 rad
magnetic flux = N*B*A*cos(theta2) = 0.090138 weber

4)
magnetic flux = N*B*A*cos(w*t)
induced emf = the rate opf change of magnetic flux
emf = d(N*B*A*cos(w*t))/dt
emf = N*B*A*w*sin(w*t)
at t = 0.45
emf = 0.47397 volts
i = emf/R = 0.47397/2.8 = 0.1693 A

5) 2nd option is true
flux = 0 and I = Imax

6) 3rd option is true

flux(max) remains same and Imax becomes double

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