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Suppose the magnetic field of the preceding problem oscillates with time according to . What then is the emf induced in the loop when its trailing side is a distance d from the right edge of the magnetic field region?
Solution
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We are given that the magnetic field varies with time with the next equation
According to Faraday's law, the induced emf is given by
Where and is the magnetic flux in the loop and it is given by equation 13.1 in the form
is perpendicular to the plane of the loop, so the dot product will convert to a multiplication of magnetic field and area where the area, in this case, will be and equation (2) will be in the form
Where and are the sides of the rectangular loop. Now let us take the derivative of equation (1) for because it is the changeable parameter
Now let us use the expression of and take the derivative for time to get the expression of
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