# Zero-Divergence of Rate of Change of Magnetic Flux

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## ?

Simon Bridge
Homework Helper
... and what do you get?

... and what do you get?
that's what I'm wondering myself

Simon Bridge
Homework Helper
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.

• berkeman
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.

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?