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What is the peak emf generated by rotating a 1000 -turn, 20.0 $\mathrm{cm}$ diameter coil in the Earth's $5.00 \times 10^{-5} \mathrm{T}$ magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms?

246.4 $\mathrm{mV}$

01:30

Averell H.

06:16

Mohammad A.

Physics 102 Electricity and Magnetism

Chapter 23

Electromagnetic Induction, AC Circuits, and Electrical Technologies

Electromagnetic Induction

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

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Electromagnetic induction …

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okay. In the given problem, the number off terms in the koi is N is equal to 1000. The diameter off the coil is given us 20 centimeter, so it's radius will be 21 0 by two centimeter means 10 centimeter. Or we can say this is 0.1 Neto. It is making 1/4 off rotation, one fourth off rotation, so its frequency will come out to be the time taken for this one. Fourth rotation is then milliseconds or we can say 10 into, and it's par minus three seconds so its frequency will come out. Toby Number off rotations, which is 1/4 and but in a time means stand into 10 days, four minus three. So it becomes 100 by four means 25 hertz, or we can say 25 r. P s revolutions per second. So if frequencies 25 revolutions per second, so it's angular. Frequency will be to buy into F means to in 23.14 in 2 25 radiant per second. So the PKF induced in the magnetic field when it is rotated in the Earth's magnetic field and the Earth's magnetic field has been given a value off five wind zero zero into 10. Dish par minus five Tesla. So finally, using the relation for the PMF induced in terms off number off terms angular velocity area of the coil and magnetic field which is equal to the product off all these four absolute not is equal to so plugging in all the values. Here we get the PMF induced to be equal to 1000 into two into 3.14 into 25 radian per second. For angular velocity, buy into our square means 0.1 to the whole square for area and five into 10 days Par minus five Tesla for the magnetic field. So finally it comes out to be zero point 246 volt. Or we can say this is 246.4 milli vault. This is the answer for the given problem. Thank you.

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