– Thomas A. Edison

Today I will give you a free response practice question on electromagnetic induction. You may try to answer this question within 15 minutes. Here is the question:

Two infinitely long straight parallel wires W_{1} and W_{2}, separated by a distance ‘*a*’ in free space, carry equal currents I flowing in opposite directions as shown in the adjoining figure. A square loop PQRS of side ‘*a*’,* *made of nichrome wire of resistance *ρ* Ω per metre is arranged with its plane lying in the plane of the wires W_{1} and W_{2} so that the sides PQ and RS of the loop are parallel to the wires W_{1} and W_{2}. The side PQ of the loop is at a distance ‘*a*’ from the wire W_{2}. Now, answer the following questions in terms of the given quantities and fundamental constants:

(a) Determine the magnetic flux density at a point midway between the wires W_{1} and W_{2}.

(b) Determine the magnetic flux density at the mid point of the square loop PQRS.

(c) Calculate the magnetic flux through the loop PQRS.

(d) What is the average emf induced in the loop when the current through the wires is switched off in a time of 50 ms?

(e) When the current through the wires is switched off, it is found that at a certain instant *t*, the current decays at the rate of 40 As^{–1}. Calculate the current induced in the loop PQRS at the instant* t*.

Indicate the direction of the current in the loop and justify your answer.

This question carries 15 points. Try to answer it. I’ll be back soon with a model answer for your benefit.

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