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I Zero-Divergence of Rate of Change of Magnetic Flux

  1. May 3, 2016 #1
    Let's introduce a time-varying scalar field ρ(x,y,z,t) [charge density] and vector field J(x,y,z,t) [current density]

    Assuming the system follows Maxwell's equations, what must both fields satisfy such that

    ##∇⋅(\frac{∂B}{∂t})=0## ?
     
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  3. May 3, 2016 #2

    Simon Bridge

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    ... and what do you get?
     
  4. May 4, 2016 #3
    that's what I'm wondering myself
     
  5. May 4, 2016 #4

    Simon Bridge

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    Well do the maths and see ... i.e. can you change the order between the time-partial and the div in that last equation?

    If I don't see how you are attempting the problem I don't know how it is a problem for you so I don't know how to help you.
     
  6. May 7, 2016 #5
    Oh I get it! Gauss' Law for Magnetic Flux! Right under my nose the whole time.
     
  7. May 7, 2016 #6
    This leads to the next part of my question, if you don't mind.

    Let's say we are given a vector field ##A##.

    Vector field ##B## is defined as ##B = ∇×A##

    Must ##∇⋅A=0## in order for ##B## to exist?
     
  8. May 7, 2016 #7

    Simon Bridge

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