# What is the curl of a electric field?

by back2square1
Tags: curl, electric, field
 P: 13 This should be simple but I know I'm going wrong somewhere and I can't figure out where. The curl of a electric field is zero, i.e. $\vec { \nabla } \times \vec { E } = 0$ Because , no set of charge, regardless of their size and position could ever produce a field whose curl is not zero. But, Maxwell's 3rd Equation tells us that, the curl of a electric field is equal to the negative partial time derivative of magnetic field $\vec {B}$. i.e. $\vec { \nabla } \times \vec { E } = -\frac { \partial }{ \partial t } \vec { B }$ So is the curl zero or is it not? If we equate those two equations we get that the time derivative of magnetic field is zero. What's wrong? What am I missing?
Mentor
P: 10,693
 Quote by back2square1 The curl of a electric field is zero, i.e. $\vec { \nabla } \times \vec { E } = 0$
That should read, "the curl of an electrostatic field is zero," that is, the electric field associated with a set of stationary charges has a curl of zero. In this situation, there is no magnetic field, so ##\partial \vec B / \partial t = 0##.
 P: 13 Oh. Thanks. Got it. Sometimes things as simple as this slip off.

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