A conducting wire formed in the shape of a right triangle with base b = 34 cm an

Question

A conducting wire formed in the shape of a right triangle with base b = 34 cm and height h = 77 cm and having resistance R = 2.2 , rotates uniformly around the y-axis in the direction indicated by the arrow (clockwise as viewed from above (loooking down in the negative y-direction)). The triangle makes one complete rotaion in time t = T = 1.6 seconds. A constant magnetic field B = 1.7 T pointing in the positive z-direction (out of the screen) exists in the region where the wire is rotating.

1) What is , the angular frequency of rotation?

2) What is Imax, the magnitude of the maximum induced current in the loop?

3) At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux 1 at time t = t1 = 0.6 s?

4) What is I1, the induced current in the loop at time t = 0.6 s? I1 is defined to be positive if it flows in the negative y-direction in the segment of length h.

5) Which of the folowing statements about o, the magnitude of the flux through the loop at time t = to = 0.4 s, and Io, the magnitude of the current through the loop at time t = to = 0.4 s, is true? max and Imax are defined to be the maximum values these quantites achieve during the complete rotation.

6)

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

Explanation / Answer

1. w = 2 pi / T = 2 pi /1.6 = 3.93 rad/s

2. Imax = e_max / R

e_max = N A B w = 1 x (0.34 x 0.77 / 2) x 1.7 x 3.93

= 0.874 Volt  

Imax = 0.874 / 2.2 = 0.397 A ........Ans

3. flux = B.A cos(w t) = 0.223 cos(3.93 t)

at t = 0.6 s

flux = - 0.158 Wb  

4. I = d(flux)/dt ) / R = - (0.223x3.93 / 2.2) sin(3.39t)

I = 0.0.243 A

5. w t = 90 deg

flux = 0

and I = Imax

6,. if f -> doubled theb

flux is independent of f so it will remain same.

Imax will also be doubled/

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