Q. 41

Expert-verifiedFound in: Page 871

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A square loop lies in the -plane. The magnetic field in this region of space is , where is in . What is the induced in the loop at and

Part

The induced in the loop is

Part

The induced in the loops is

The induced emf in the loop is equivalent to the weight of the rate of change of the magnetic flux through the loop, according to Faraday's law of induction. The derivative of the magnetic flux with respect to time equals this rate of change, thus

Now that the loop is in the plane, the loop's normal is the -axis, this means that the plane's normal unit vector. As an outcome, only the component along contributes to the transit across the loop:

where is the area of the loop and is its side.

Taking the derivative we obtain

Returning this into equation we get

(a) Set into the expression for to get

(b) Set into the expression for to get

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