Well we start out with(adsbygoogle = window.adsbygoogle || []).push({});

[tex]-\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi}[/tex]

Using the Gauss theorem

[tex]\int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0[/tex]

so

[tex]\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0[/tex]

and written in 4D..

[tex]\frac{ \partial {J^n}}{ \partial {x^n}} = 0 \qquad\quad\ (n = 0,1,2,3)[/tex]

I can't seem to get my head around that last step. How does it expand out?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Deriving the 4d continuity equation

**Physics Forums | Science Articles, Homework Help, Discussion**