Answer to Question #107076 in Electricity and Magnetism for Vitezslav Havelek

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

Just write an expression for the induced voltage of a moving conductor in a magnetic field parpendicullar to magnetic field lines:

$$E=-Blv.$$

The induced electromotive force does not depend on the cross-sectional area of the conductor, so, the voltage will be

$$V=-E=1\cdot1\cdot1=1\text{ V}.$$