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A 100-turn square wire coil of area 0.040 $\mathrm{m}^{2}$ rotates about a vertical axis at 1500 $\mathrm{rev} / \mathrm{min}$ , as indicated in Figure $\mathrm{P} 20.32 .$ The horizontal component of Earth's magnetic field at the location of the loop is $2.0 \times 10^{-5} \mathrm{T}$ . Calculate the maximum emf induced in the coil by Earth's field.

0.0126 \mathrm{V}

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our question asks us to calculate the maximum induced E M F in the coil by Earth's magnetic field, So the induced E m F in a coil here is going to be equal to the number of turns in the coil times the magnetic field times the area of the coil times the rotation omega. We're told this is 1500 revolutions per minute, while one revolutionist to pie. So you multiply 1500 by two pie and then one minute is 60 seconds. They divide by 60 and that gives you radiance per second. So omega is 157 radiance percentage. And then this is also multiplied by the sign of omega T. But he is at maximum. So we'll say, Max, um, sine omega t equal the one right, because sign of value is gonna give you something between zero and one. So it's gotta be maximum when this is equal to one. So therefore, the induced M f will call this CMF. Max is equal to the number of turns times the magnetic field times, the area times omega. Plugging those values into this expression, we find that this is equally 12 12.6 times 10 to the minus three in the units here, of course, are volts. So we can go ahead and box 12.6 10% of minus three volts in as the solution to their questions.