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Deriving electric field strength in terms of retarded potentials

  1. Dec 3, 2011 #1
    since, B=curl(A), curl(E)= -[itex]\partial[/itex]B/[itex]\partial[/itex]t
    1)curl(E)=- [itex]\partial[/itex]/[itex]\partial[/itex]t(curl(A))
    2)curl( E+[itex]\partial[/itex]A/[itex]\partial[/itex]t)=0
    3)then since curl([itex]\nabla[/itex]V)=0,

    E +[itex]\partial[/itex]A/[itex]\partial[/itex]t =- [itex]\nabla[/itex]V
    E= -[itex]\nabla[/itex]V -[itex]\partial[/itex]A/[itex]\partial[/itex]t

    I'm confused about how to go from step 1 to step 2. The first thing I did was add the right side to the left to get: curl(E)+[itex]\partial[/itex]/[itex]\partial[/itex]t(curl(A))=0

    I know there's a property that says
    a X (b+c) = a X b + a X c

    But what about the -[itex]\partial[/itex]/[itex]\partial[/itex]t ? How would I deal with that?

    Thank you.

    edit: perhaps this should be in the calculus section?
    Last edited: Dec 3, 2011
  2. jcsd
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