relativity_14 - PHY2061 R. D. Field Electric Field of a...

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PHY2061 R. D. Field Department of Physics relativity_14.doc University of Florida Electric Field of a Moving Charge Particle Consider a point charge Q at rest at the origin in the O'-frame and consider the electric field in the O-frame at the moment the origins of the two frames coincide (t = t' = 0). We know that, r r KQ E = ˆ ) ( 2 ! . In the O'-frame : 2 / 3 2 2 2 2 / 3 2 2 2 ) ( sin ) ( ) ( cos ) ( y x y KQ r KQ E y x x KQ r KQ E y x + = = + = = θ 2 2 / sin / cos y x r r y r x + = = = In the O-frame : 2 2 / sin / cos y x r r y r x + = = = 2 1 / 1 / β γ = = c V 2 / 3 2 2 2 2 2 / 3 2 2 2 2 / 3 2 2 2 / 3 2 2 2 2 2 / 3 2 2 2 2 / 3 2 2 ) sin 1 ( sin ) 1 ( ) ( ) ( ) sin 1 ( cos ) 1 ( ) ( ) ( = + = +
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