A conducting wire formed in the shape of a right triangle with base b = 22 cm an

Question

A conducting wire formed in the shape of a right triangle with base b = 22 cm and height h = 85 cm and having resistance R = 1 , 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 = 1.4 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.

HELP PLEASE! Thank you!

Explanation / Answer

a. angular frequency W = 2pi/t

W = 2*3.14/1.6 = 3.926 rad/s

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induced emf e = NABW

emf e = 1 * (0.5 b h ) * 1.4 * 3.926

emf e = 1 * 0.5 * 0.22* 0.85 * 1.4 * 3.926

emf e = 0.513 Volts

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3. magnetic flux phi = NAB Cos wt

phiB = 1.4 * 0.5* 0.22* 0.85 * cos (3.926 *0.6)

flux = 0.0925 Wb

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4. induced emf e = NAbW sin Wt

emf e = 1.4 * 0.5* 0.22* 0.45 * 3.926 * sin (3.926 * 0.6)

emf e = 0.1924 Volts

induced current i = emf/R = 0.1924/1 = 0.192 Amps

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