0
$\begingroup$

In electrostatics, we know that $\vec{\nabla}\times\vec{E} = 0$ and so, the field lines can't form loops. But when we have time-dependant magnetic fields, there's the Faraday-Lenz law which tells us that $\vec{\nabla}\times\vec{E} = -\frac{\partial\vec{B}}{\partial{t}}$. Does that mean that we can have closed field lines for the electric field, let's say for example, when we have moving magnets?

If that's the case, can you have closed field lines in another way that isn't with time-dependant magnetic fields?

Improve this question
$\endgroup$
2
  • $\begingroup$ I've found in some places that this seems to be the case, but I just want to make sure. :D $\endgroup$
    – D. Sarrat
    Commented May 24, 2022 at 19:51
  • $\begingroup$ One of the cooler applications of closed electric field lines is the betatron (en.wikipedia.org/wiki/Betatron). It does, however, require a changing magnetic field. $\endgroup$
    – John Doty
    Commented May 24, 2022 at 20:14

1 Answer 1

Reset to default
1
$\begingroup$

In short:

Does that mean that we can have closed field lines for the electric field, let's say for example, when we have moving magnets?

Yes.

If that's the case, can you have closed field lines in another way that isn't with time-dependant magnetic fields?

No.

I've found in some places that this seems to be the case

Either you're misreading those situations or there is a time dependent magnetic field, but it's obviously impossible to say without more information.

Improve this answer
$\endgroup$
1
  • $\begingroup$ With "I've found in some places that this seems to be the case" I was referring to the fact that there's closed electric field lines, not that there is without changing B. I understand that if B does not change in time, curl(E) = 0 and it's the same as in electrostatics. Thanks for the answer! $\endgroup$
    – D. Sarrat
    Commented May 24, 2022 at 20:30

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.