# What is the curl of a electric field?

1. ### back2square1

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?

### Staff: Mentor

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##.

3. ### back2square1

13
Oh. Thanks. Got it. Sometimes things as simple as this slip off.