Rotate a 40-turn rectangular loop that is 0.1 m by 0.2 m in a uniform magnetic field of 2 teslas, turning at a rate of 30 revolutions (2π radians) per second. What is the maximum emf?
emf= omega*B*(Area)*sin(omega*t)
I'm not sure how to plug in numbers correctly. The book I have does a poor job of explaining it.
The answer is 302 volts, I need to know how to get the answer.
Thanks!
emf= omega*B*(Area)*sin(omega*t)
I'm not sure how to plug in numbers correctly. The book I have does a poor job of explaining it.
The answer is 302 volts, I need to know how to get the answer.
Thanks!
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Basically, when the loop is turning, it is going from maximum flux to minimum flux. Flux is the amount of magnetic field lines that cut through the area of the loop. Maximum flux occurs when the area of the loop is perpendicular to the magnetic field, and minimum flux occurs when the area of the loop is parallel to the magnetic field. This change in magnetic field causes an induced emf according to Faradays law.
Maximum emf occurs at the maximum change in flux in a given time.
Flux changes from 0 to maximum ( sin(omega*t) = 1 ).
So:
max. emf = (number of coils) * omega*B*(Area)*sin(omega*t)
max. emf = (number of coils) * omega*B*(Area)
max. emf = 40 * 30 * 2π * 2 * 0.1 *0.2 = 302 volts ------ Answer
Maximum emf occurs at the maximum change in flux in a given time.
Flux changes from 0 to maximum ( sin(omega*t) = 1 ).
So:
max. emf = (number of coils) * omega*B*(Area)*sin(omega*t)
max. emf = (number of coils) * omega*B*(Area)
max. emf = 40 * 30 * 2π * 2 * 0.1 *0.2 = 302 volts ------ Answer