# Curl of Induced E Field?

I have a problem. So the curl of the E field is supposed to be zero always, which tells us that it is a conservative force (path independence and scalar potential and so on). But what about the fact that the induced electric field consequent upon changes in magnetic flux is circular? Doesn't this mean that if we sustained such a field we would have a non-conservative electric field?

Is this a problem, or is it just that the claim about electric fields having zero curl has application only to electrostatics?

## Answers and Replies

MarcusAgrippa
Gold Member
I have a problem. So the curl of the E field is supposed to be zero always, which tells us that it is a conservative force (path independence and scalar potential and so on). But what about the fact that the induced electric field consequent upon changes in magnetic flux is circular? Doesn't this mean that if we sustained such a field we would have a non-conservative electric field?

Is this a problem, or is it just that the claim about electric fields having zero curl has application only to electrostatics?
The curl of the E-field is zero only if the E-field is time independent, i.e. electrostatics. In the dynamic case, the curl of the E-field is the negative rate of change of the B-field, which is not zero in general. This makes the dynamic E-field non-conservative, with the path integral around a closed loop equal to the EMF in the circuit which drives the current.

Dale
Mentor
2020 Award
the curl of the E field is supposed to be zero always
No, ##\nabla \times E=-\partial B/\partial t##

Last edited:
MarcusAgrippa
Gold Member
No, ##\nabla \times E=\partial B/\partial t##
Don't forget the negative sign.

Dale
Mentor
2020 Award
Don't forget the negative sign.
Oops, fixed it.