# What is the curl of a electric field?

• back2square1
In summary, the conversation discusses the concept of the curl of an electric field, with one person questioning whether it is zero or not. It is clarified that the curl of an electrostatic field is indeed zero and there is no magnetic field present. The confusion is resolved by understanding that in this situation, the time derivative of the magnetic field is also zero.
back2square1
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?

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.

## 1. What is the definition of the curl of an electric field?

The curl of an electric field is a mathematical operation that describes the rotational behavior of the field. It is a vector quantity that indicates the strength and direction of the rotation at a specific point in the electric field.

## 2. How is the curl of an electric field calculated?

The curl of an electric field can be calculated using a mathematical formula involving partial derivatives of the electric field components. This formula is known as the curl operator or del cross operator and is represented by the symbol ∇ x.

## 3. What does a non-zero curl of an electric field indicate?

A non-zero curl of an electric field indicates that the field is not conservative, meaning that its path is dependent on the direction of movement. This can occur in cases where there is changing magnetic flux or non-static charges present in the electric field.

## 4. Can the curl of an electric field be negative?

Yes, the curl of an electric field can be negative. The sign of the curl depends on the direction of the rotation at a specific point in the electric field. A negative curl indicates a clockwise rotation, while a positive curl indicates a counterclockwise rotation.

## 5. How is the curl of an electric field used in scientific research?

The curl of an electric field is an important concept in electromagnetism and is used extensively in scientific research, particularly in the fields of electrical engineering, physics, and geophysics. It is used to study the behavior of electric fields and to solve complex problems involving electric fields in various applications.

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