What is the curl of a electric field?

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The curl of an electric field is zero in electrostatic conditions, meaning that stationary charges produce an electric field with no curl. However, according to Maxwell's third equation, the curl of an electric field can be non-zero when there is a changing magnetic field, represented by the equation ∇ × E = -∂B/∂t. In situations where the magnetic field is not changing, the time derivative of the magnetic field is zero, confirming that the curl of the electric field remains zero. The confusion arises when distinguishing between static and dynamic cases of electric fields. Understanding this distinction clarifies the conditions under which the curl of an electric field is zero or not.
back2square1
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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?
 
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back2square1 said:
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##.
 
Oh. Thanks. Got it. Sometimes things as simple as this slip off.
 
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