| MadSci Network: Physics |
Two electrons moving with velocities (any velocities, not necessarily relativistic) that are not collinear will experience more force than two stationary electrons at the same distance and same instantaneous positions, and for two reasons: 1) the electric field of the electron perpendicular to the direction of travel is enhanced by the gamma factor where gamma=(1-v^/c^2)^-1/2. Since the gamma factor grows monotonically with speed, faster electrons will feel more force than slow electrons. By the way, the component of the electron's electric field along the direction of travel does not change under a Lorentz boost. This is not the way that a 4-vector like, say, momentum behaves under boost, but that's because the electric field is not a 4-vector. The electric and magnetic fields transform as an antisymmetric rank-2 tensor under boosts. http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity 2) Moving charges produce magnetic fields whereas the stationary electric charges do not. One electron will therefore feel an unenhanced electric field along the direction of motion, an enhanced electric field perpendicular to the direction of motion, and a magnetic field that was zero in the stationary case. This answer assumes that the electric and magnetic fields of one electron have had enough time to propagate at the speed of light to the other electron. So, for example, if you start with two electrons a lightyear apart (according to some observer), they will not feel each other for a year (according to that same observer). --Randall J. Scalise http://www.physics.smu.edu/scalise
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