Marin, a 17 year old male from Split, Croatia asks on August 23, 2002,What happens when electrons pass through a magnetic field at a velocity near lightspeed?
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The first answer is that the electron path is bent by the magnetic field (the familiar evxB force of a magnetic field on an electron). If the field is large enough, then one could also get electron positron pairs created-- but this would require a field such that the synchrotron radiation produced by the electron on its non straight line path has a frequency approaching that needed to produce electron-positron pairs.
Note that the electrons seen as decay products in particle accelerators are detected precisely from the curvature of the tracks produced by the (highly relativistic) electrons in the magnetic fields of the detectors.
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