# I Zero-Divergence of Rate of Change of Magnetic Flux

1. May 3, 2016

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

$∇⋅(\frac{∂B}{∂t})=0$ ?

2. May 3, 2016

### Simon Bridge

... and what do you get?

3. May 4, 2016

that's what I'm wondering myself

4. May 4, 2016

### Simon Bridge

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.

5. May 7, 2016

Oh I get it! Gauss' Law for Magnetic Flux! Right under my nose the whole time.

6. May 7, 2016

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?

7. May 7, 2016