relativity_19 - PHY2061 R. D. Field Interaction of a Moving...

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PHY2061 R. D. Field Department of Physics relativity_19.doc University of Florida Interaction of a Moving Charge with other Moving Charges – Case II Lab Frame (O-frame): Charge particle Q moving to the right with velocity V. Neutral wire with current I = λ + V moving to the left with λ = λ + - λ - =0, where λ is the net charge density of the wire. Particle experiences a “magnetic” force F. Particle Frame (O'-frame): Charge particle Q at rest. Wire is now positively charged with λ ' = λ ' + - λ ' - >0, and the particle experiences an electric field, E' = 2K λ '/r' and an (repulsive) electric force F’ = 2KQ λ '/r'. Calculate the force in the lab frame from knowledge of the electric force in the particle frame! Lab Frame: 0 0 0 = = = = + + + λ γλ + + + = = = 0 0 0 γβλ c V I Particle Frame: + + + + + = = = = = 0 2 2 0 2 0 0 ) ( γ β ) 1 ( ) 1
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