Electric Eddy Field: Calculating with Maxwell's Equations

[hildebrand]

Hello!

I'm studying Maxwell's equations at the moment. To solve Maxwell's equations one can introduce scalar- and vectorpotentials and calculate the electric and magnetic field by $$E=-\text{grad}\,\Phi-\frac{\partial A}{\partial t}$$
and
$$B=\text{rot}\,A$$,
respectively.
I have the following question to that: Is the contribution of the time derivative of $$A$$ in the formula for $$E$$ due to the electric eddy field that is induced by a time varying magnetic field? If not, how it is possible to calculate the electric eddy field when a time varying magnetic field is given?

Thank you for your help!

 

[Meir Achuz]

The term "electric eddy field" is not commonly used in English. Just saying "electric field" is enough. If you take
$$\text{rot}\,E=\text{rot}[-\text{grad}\,\Phi-\frac{\partial A}{\partial t}]$$, you get Maxwell's equation that is differential equation relating E and B.