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Unformatted text preview: the gamma, ( P γx , P γy , P γz ) /P γ ? 3) Given ﬁelds, E = E (1 , x/R, x 2 /R 2 ) e x , where E is constant. Perform the surface integral R S da E · n for each ﬁeld, where S is the surface of a sphere of radius R and n is the outward unit vector perpendicular to the surface? 1 4) A , B are arbitrary vectors that can be functions of the coordinates? Prove, ∇ ( A · B ) = ( A · ∇ ) B + ( B · ∇ ) A + A × ( ∇ × B ) + B × ( ∇ × A ) . (2) Use this result to prove, ∇ ( r · B ) = B + r ( ∇ · B ) + ( r × ∇ ) × B , (3) where r is the usual position vector. The quantityi ( r × ∇ ) is the angular momentum operator in quantum mechanics. 2...
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.
 Spring '10
 Blecher
 Charge, Magnetism

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