0
$\begingroup$

Induced electric field in a changing current solenoid

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

image creditis: https://faculty.uml.edu//Andriy_Danylov/Teaching/documents/L18Ch33InducedEcovered.pdf

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.

$\endgroup$

1 Answer 1

1
$\begingroup$

The magnetic vector potential isn't the induced electric field. However, in the case that the net charge density $\rho = 0$

The induced electric field can be expressed purely in terms of the magnetic vector potential.

$\vec{E} = - \frac{\partial \vec{A}}{\partial t}$

Infact, given the net charge density is not zero, this equation can also be used to find the induced solenoidal component of the E field, provided we are in the coulomb gauge.

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.