Question

Some documents define an electrostatic field as the electric field of a stationary charge or steady current.

However, in other documents, they are defined them as electric fields satisfying ∇ × E⃗ = 0.
And another defines them as electric field that do not change with time.
I know that the case in 1,3 implies that case 2 (maybe 3 implis 2).

But, I think any case that corresponds to 3 may not correspond to 1 or 2.

Thus, I think the above 3 definitions are not exactly the same.

is there anything I think wrong? Or, please give me the exact definition.

Answer 1

The electrostatic field can be defined as the electric field of a stationary charge or steady current, an electric field that satisfies ∇ × E⃗ = 0, or an electric field that does not change with time. While the first and third definitions imply the second, not all cases that correspond to the third definition necessarily correspond to the first or second definitions.

Step-by-step explanation:

The three definitions you mentioned are related but have some differences.

Therefore, while the case 1 and case 3 definitions imply case 2, not all cases that correspond to definition 3 necessarily correspond to definitions 1 or 2. The three definitions have similarities but also capture different aspects of the electrostatic field.