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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: $$\nabla\times {\bf B} = \mu_0 \left( {\bf J}+\epsilon_0\frac{\partial {\bf E}}{\partial t} \right)$$

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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Think of a parallel plate capacitor as it charges.

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.

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  • $\begingroup$ @mathreadler, you're welcome. Please accept the answer if you are satisfied with it. $\endgroup$ – user1936752 Jan 27 at 16:01
  • $\begingroup$ I have a principle of never accepting answer until after 24 hours. To not discourage other people from answering. $\endgroup$ – mathreadler Jan 27 at 16:12
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There is also a case in which $\nabla \times B =0$, in which case $J$ and $\frac{\partial {\bf E}}{\partial t}$ are proportional.

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  • $\begingroup$ But the OP is asking about the difference between these two terms. In classical mechanics force and acceleration are proportional, but saying this doesn't tell me what differentiates the two things. $\endgroup$ – Aaron Stevens Jan 29 at 5:27
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$\partial \mathbf E / \partial t$ 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).

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