relativity_22 - the classical formula(approximation ˆ ˆ 2...

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PHY2061 R. D. Field Department of Physics relativity_22.doc University of Florida Force Between Two Moving Charged Particles Consider the force on q moving with velocity v due to Q moving with velocity V . The moving charge Q produces both an electric and magnetic field given by E V c B r r KQ E ! ! ! ! × = = 2 2 / 3 2 2 2 2 1 ˆ ) sin 1 ( ) 1 ( θ β where β = V/c, which produce a force on q given by B v q E q F ! ! ! ! × + = and thus ) ˆ ( ) sin 1 ( ) 1 ( ˆ ) sin 1 ( ) 1 ( 2 / 3 2 2 2 2 2 2 / 3 2 2 2 2 r V v r c KqQ r r KqQ F × × + = ! ! ! Classical Result: If is assume that v << c and V << c then we arrive at
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Unformatted text preview: the classical formula (approximation) ) ˆ ( ˆ 2 2 2 r V v r c KqQ r r KqQ F F F B E × × + = + = ! ! ! ! ! where B v q r V v r kqQ F E q r r KqQ F B E ! ! ! ! ! ! ! × = × × = = = ) ˆ ( ˆ 2 2 with k = K/c 2 and ) ˆ ( ˆ 2 2 r V r kQ B r r KQ E × = = ! ! ! r r q Q V v θ Classical Approximation...
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