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Q. 41

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 871

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Short Answer

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

See the step by step solution

Step by Step Solution

Step: 1 Faraday's Law of Induction:

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:

Step: 2 Derivative Portion:

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

Taking the derivative we obtain

Returning this into equation we get

Step: 3 Finding the values: (part a and part b)

(a) Set into the expression for to get

(b) Set into the expression for to get

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