EMF of a square conductor moving in homogeneous magnetic field

Question

We have a homogeneous magnetic field of strength 1T.

There is a copper SQUARE conductor, moving by constant speed 1m/s in a direction parpendicullar to magnetic field lines, so we can measure inducted electromotive force at the terminal ends of a conductor.

Effective length of a conductor inside a field is 1m.

What is the voltage measured between conductor terminals if:

1) Width of conductor is 1cm, height is 1mm

2) Width of conductor is 1mm, height is 1cm

3) Width and height of conductor is 1mm x 1mm (the length is 1m in all three cases)

Answer 1

This problem is an application of Faraday's Law of Induction.

As the problem is worded the answer to each part is 0 V. The key is that the problem only discusses the loop moving in a magnetic field, not from a region with 0 magnetic field to the field given! Faraday's Law states that the induced electric voltage is due to the CHANGE in the magnetic flux in the loop. In this case since the magnetic field is constant, there is no change in the flux.

On the other hand let's assume that the writer of the problem intended us to believe that the rectangular loop was going from a region of NO magnetic field to one with the given field. The total magnetic flux will be the sum of 0 for the part outside the magnetic field and B x height x length within the field. This is a common problem in the course and gives a result that the emf/voltage will be B x height x speed of the loop as it enters the magnetic field. Don't forget to convert units to mks.