Zero-Divergence of Rate of Change of Magnetic Flux

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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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  • #2
Simon Bridge
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... and what do you get?
 
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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.
 
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  • #5
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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.
Oh I get it! Gauss' Law for Magnetic Flux! Right under my nose the whole time.
 
  • #6
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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?
 

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