# Is the induced electric field in a current changing solenoid actually that what we call magnetic vector potential field?

Induced electric field $$E$$ in a changing current (i.e. changing magnetic field $$B$$) solenoid

I was wondering if the induced electric field $$E$$ in that case is actually referring and identical to the magnetic vector potential $$A$$ field around a magnetic field $$B$$ source. Therefore, the mathematical concept in physics and electromagnetism of magnetic vector potential field $$4$$ can be physically interpreted, as what the induced electric field would be by a magnetic field if this was changing with time?

WP seems to support this interpretation in its given definition for the magnetic vector potential, quote:

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: $${\textstyle \nabla \times \mathbf {A} =\mathbf {B} }$$. Together with the electric potential $$φ$$, the magnetic vector potential can be used to specify the electric field E as well.

The magnetic vector potential isn't the induced electric field. However, in the case that the net charge density $$\rho = 0$$
$$\vec{E} = - \frac{\partial \vec{A}}{\partial t}$$