# Difference between $\bf J$ and time derivative of $\bf E$ in Maxwells equations? [closed]

Maybe I am being confused. It was some years ago I did this. An electric current changes charge distribution which creates rotation in $$\bf B$$. So in Ampères / Biot-Savarts law what is the difference between $$\bf J$$ and the time derivative of $$\bf E$$ field? Is one of them change of $$\bf E$$ field which could be explained except for a current or other way around?

Here is the version of equation which I am looking at: $$\nabla\times {\bf B} = \mu_0 \left( {\bf J}+\epsilon_0\frac{\partial {\bf E}}{\partial t} \right)$$

## closed as unclear what you're asking by FGSUZ, ZeroTheHero, Buzz, Jon Custer, glSJan 31 at 12:38

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The electric field across the capacitor changes but there is no current between the parallel plates. The only way to explain the magnetic field between the plates is using the $$\frac{\partial{E}}{\partial t}$$ term.
There is also a case in which $$\nabla \times B =0$$, in which case $$J$$ and $$\frac{\partial {\bf E}}{\partial t}$$ are proportional.
$$\partial \mathbf E / \partial t$$ represents the rate of change of the electric field $$\mathbf E$$ at that point. Electric fields do not need to change at a point due to movement of charges at that point. For example, consider the space between the plates of a charging capacitor (moving charges are nearby, but not at that point) or consider electromagnetic waves travelling through a vacuum (no moving charges are present at all).