Calculating Induced Voltage in a Rotating Rectangular Loop

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The discussion focuses on calculating the induced voltage in a rotating rectangular loop measuring 40cm by 30cm, which rotates at 130 revolutions per second in a magnetic field of 0.06 T. The loop consists of 50 turns, and the user applied the formula involving the magnetic field and the geometry of the loop, resulting in an induced voltage expression of 46.8 sin(130t). However, the expected answer from the textbook is -54 V, indicating a discrepancy that suggests the need for further verification of the calculations and understanding of time-varying voltage in a constant magnetic field.

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A 40cmX30cm rectangular loop rotates at 130 r/s in a magnetic field of .06 in the direction normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop.

Heres what I did. I used B dot ds. I had my ds being the sides of the rectangle and coswt in the normal direction. I then took the derivative of that. So I multiplied 130*.4*.3*50*.06. The 50 comes from the number of turns.
I ended up with an answer of 46.8 sin 130 t. The book has an answer of -54. Since the magnetic field is unchanging, the voltage has to be time-varying.
 
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can somebody confirm my answer?
 
Looks right, and yes, the voltage should definitely oscillate.
 

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