The figure shows a stationary conductor, whose shape is similar to the letter \"

Question

The figure shows a stationary conductor, whose shape is similar to the letter "e" (a = 49.9 cm), that is placed in a constant magnetic field of magnitude B = 0.560 T directed out of the page.

http://www.solutioninn.com/images/P-M-F-L%20(68).PNG

A 49.9 cm long, straight conducting rod pivoted about point O rotates with a constant angular speed of 2.28 rad/s. Determine the induced EMF in loop POQ.

If the conducting material has a resistance per unit length of 5.30 ?/m, what is the magnitude of the induced current in loop POQ at t = 0.230 s?

Explanation / Answer

area of "loop" is like a piece of pie, with angle @.

The area is given by area = (1/2) @ a^2

In this case, at t = 0.230s, the angle is @ = 2.28 rad/s * 0.230s = 0.5244 radians

Now, the length of the loop is given by a + a + a@ = 0.499 + 0.499 +0.499*0.5244 =

= 1.2597 meters

so the resistance is 5.30 * 1.2597 = 6.676 ohms

The induced voltage is voltage = B * rate of change of area =

= B * (1/2) a^2 d@/dt = 0.560 * (1/2) * 0.499^2 * 2.28 =

= 0.15896 volts

and the induced current is current = voltage / resistance = 0.15896 V / 6.676 ohms =

= 0.02381 amps = 23.81 mA

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