Question

In wikipedia about electric field, it define electrostaatic field as electric fields that do not change with time.

And article about electric potential, it define electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V.

But i'm not convinced about they mean same thing, exactly. E = -∇V means that electric field dosen't change with time?

Or there is good definition of electrostatic field?

Answer 1

An electrostatic field is a static electric field that does not change with time, coming from fixed charge distributions. It's represented as a vector field derived from the negative gradient of the scalar electric potential, denoted by V. E = -∇V does not imply a time change but spatial variation.

Step-by-step explanation:

The electrostatic field is a special case of the electric field where the electric field is constant or does not change with time. It arises from fixed charge distributions and can be represented both as a vector field and in terms of the electric potential V, which is a scalar quantity.

The relationship E = -∇V indicates that an electrostatic field can be derived as the negative gradient of the electric potential, with the negative sign indicating that the electric field points in the direction of decreasing potential.

In simple terms, the presence of the gradient in E = -∇V does not imply anything about the electrostatic field changing over time. Instead, it describes how the electric field varies in space. Hence, an electrostatic field can be said to be described by this equation when it is not changing in time and is only due to static charges.

To summarize, an electrostatic field is one that is static—meaning it does not change over time. In contrast, electric fields resulting from changing magnetic fields are dynamic and do not have an associated electric potential in the same way.