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Wednesday, April 25, 2012

Moving a Conducting Rod through a B-field

Here's a case where by simply moving a metal stick through a magnetic field, the stick acts like a battery. The idea is that because it is a conductor, the rod has free electrons. By moving it in a B-field, we will have F = qv x B kick in. This causes the rod to become polarized, with one end positive and one end negative. But think about what else is set up if one separates charge on an object - you would have a voltage difference between the two ends. And if there is a voltage difference across a conductor, E = -dV/dr tells use there is an E-field running through the rod. This E-field produces an electric force on those same delocalized electrons. So a magnetic force points one way, and an electric force points in the opposite direction. At some point the electric force will balance the magnetic force, as long as the speed of the rod remains constant: qE = qvb.

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