The Student Room Group

Divergence theorem

I learned the continuity equation.
▽(Dot)J = - partial (lo)v / partial t

I just thought about the things learned last time and remembered divergence theorem and it looks like I can put (sigma)E instead of J.
But the result was not right. I think this may not work. Do you know why it doesn't work? Or where I made a mistake?
Original post by KoreanStudent
I learned the continuity equation.
▽(Dot)J = - partial (lo)v / partial t

I just thought about the things learned last time and remembered divergence theorem and it looks like I can put (sigma)E instead of J.
But the result was not right. I think this may not work. Do you know why it doesn't work? Or where I made a mistake?


Hi, it doesn't work because the J takes into account the total current density, whereas the relation between J and E takes into account only the free current density.

Jfree=σE\vec{J_{free}} = \sigma \vec{E}
J=Jfree+Jbound\vec{J} = \vec{J_{free}} + \vec{J_{bound}}

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