Qx) A square loop of wire 15 cm on a side is rotated uniformly about an axis thr

Question

Qx) A square loop of wire 15 cm on a side is rotated uniformly about an axis through its center and parallel to two sides. The loop rotates at a constant rate of one revolution every 45 ms in a uniform magnetic field B that is perpendicular to the axis of rotation. Because of the loop’s rotation, a sinusoidal emf is induced in it, having an rms amplitude of 70 mV. Based on this information, how strong is the magnetic field? Include a sketch of the set up.

Hints for Qx:
? You may not substitute ?F/?t in place of dF/dt.
? When you write down your flux, make use of the fact that the angle between the area vector A and the field vector B is ? = ?t, where ? is the angular speed of the coil in radians per second. And ? is something that you can determine.
? Since ? depends on time, flux F also depends on time.
? Use calculus to find dF/dt.
? When you have finally arrived at a sinusoidal expression for emf, examine it to learn the peak amplitude of the sine wave (epeak), with the B left as an unknown.
? Review you notes about how peak and rms values are related, then solve for B.
? If you’re stuck, read the book’s section on electric generators.

Explanation / Answer

emf=-d/dt=-BdA/dt

==>.07=-BA/2

time period=.045s

=139.55

-B=.07*1.414/139.55*.15^2

=.0315T

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