4. A rectangular loop of wire as it is moved through a region of uniform magneti

Question

4. A rectangular loop of wire as it is moved through a region of uniform magnetic field B at velocity v. The figure below shows three snapshots of this motion:

i. half of the loop has entered the region

ii. the loop is at the midpoint of the region.

iii. half the loop has exited the region.

a) the induced current through the loop when in position i is measured to be I.

What is the value of the induced current at position ii?

What is the value of the induced current at position iii?

B) if velocity is to remain constant, in what position, if any would it be necessary to apply an external force? explain.

4. A rectangular loop of wire as it is moved through a region of uniform magnetic field B at velocity v .The figure below shows three snapshots of this motion i. half of the loop has entered the region ii. the loop is at the midpoint of the region iii. half the loop has exited the region 11 a. The induced current through the loop when in position i is measured to be I What is the value of the induced current at position ii? What is the value of the induced current at position iii? b. If is to remain constant, in which positions, if any, would it be necessary to apply an external force? Explain

Explanation / Answer

(a)

From the Faraday’s law of induction, the emf induces in a loop the magnetic flux changes through it with time.

When entering or leaving the loop, the magnetic flux through it increases or decreases respectively with time of same magnitude. Hence, the rate of magnetic flux in the position (i) and in the position (iii) is same in magnitude. Hence, the induced current in the loop in position (iii) is same as that of position (i) that is equal to I. The direction of current flow in position (iii) is clockwise.

There will be no flux changes with time in position (ii) as the loop moving with constant speed. Hence, there will be no emf induces in the loop. Hence, the amount of induced current flow through the loop in position (ii) is zero.

(b)

The magnetic forces act on the loop when current passes through it. Hence, there will be no magnetic force acts on the From the Lenz’s law, the magnetic forces on the loop due to induced current in the loop opposes the motion of the loop. Hence, to move the loop with constant speed. A force of same magnitude of magnetic force should be applied on the loop to move the loop with constant speed.

Thus, the external force should be applied on the loop in position (i) and position (iii).

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