Electrostatic charges in v x B fields: The Faraday disk and the rotating sphere
Below is a snippet in the above publication.
1. Introduction
Imagine a body that moves at velocity v in a region where there exist an electric field E and a magnetic field B. Then an electric charge Q inside the body feels a force Q(E + v x B). Thus, inside the moving body, the v x B field acts like the electric field of a distributed source. We are concerned here with conducting media that move in magnetic fields. We shall see that they carry electrostatic charges whose field is just as important as v x B. Indeed, there are many cases where the two fields cancel each other exactly at every point. The Faraday disk and a conducting sphere rotating in a magnetic field will serve as examples, but this little known effect plays a fundamental role in magnetohydrodynamics.
2. Electrostatic charges in v x B fields
It is well known that conductors do not support an electric space charge; any extra charge deposited inside moves out to the periphery almost instantaneously (Lorrain et al 1988, p 75). However, few physicists realise that conductors do carry an electric space charge when subjected to a v x B field whose divergence is not equal to zero. If the conductor is isolated, then it also carries a compensating surface charge.
GB
Below is a snippet in the above publication.
1. Introduction
Imagine a body that moves at velocity v in a region where there exist an electric field E and a magnetic field B. Then an electric charge Q inside the body feels a force Q(E + v x B). Thus, inside the moving body, the v x B field acts like the electric field of a distributed source. We are concerned here with conducting media that move in magnetic fields. We shall see that they carry electrostatic charges whose field is just as important as v x B. Indeed, there are many cases where the two fields cancel each other exactly at every point. The Faraday disk and a conducting sphere rotating in a magnetic field will serve as examples, but this little known effect plays a fundamental role in magnetohydrodynamics.
2. Electrostatic charges in v x B fields
It is well known that conductors do not support an electric space charge; any extra charge deposited inside moves out to the periphery almost instantaneously (Lorrain et al 1988, p 75). However, few physicists realise that conductors do carry an electric space charge when subjected to a v x B field whose divergence is not equal to zero. If the conductor is isolated, then it also carries a compensating surface charge.
GB
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