A conducting wire formed in the shape of a right triangle wi

A conducting wire formed in the shape of a right triangle with base b = 28 cm and height h = 82 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 (loooking down in the negative y-direction)). The triangle makes one complete rotaion in time t = T = 1.1 seconds. A constant magnetic field B = 1.1 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?

radians/second

2)

What is I_max, the magnitude of the maximum induced current in the loop?

A

3)

At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux ₁ at time t = t₁ = 0.4125 s?

T-m²

4)

What is I₁, the induced current in the loop at time t = 0.4125 s? I₁ is defined to be positive if it flows in the negative y-direction in the segment of length h.

A

Solution

angular frequency w = 2 pi / T = 2 pi / 1.1

= 5.71 rad/s

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I_max = (0.5 * a b B w) / (R)

I_max = (0.5 * 0.28 * 0.82 * 1.1 * 5.71) / (2.7)

= 0.27 A

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c) phi_B = 0.5 a b B cos (w t₁)

= 0.5 * 0.28 * 0.82 * 1.1 cos (5.71 * 0.4125)

= 0.126 T.m²

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I₁ = I_max * sin (w t₁)

= 0.011 A