When a vector field has a non zero curl, the curl might describe a magnetic field also implying the presence of an electric field. This question is about vector fields with curl of zero.

Gradient of a gravity field is one example of a curl free vector field, in this case a vector potential field.

Another type of curl free field is a Poynting vector field made from electromagnetic antennas making interference patterns in which all the electric and magnetic components have been canceled out while the Poynting energy flux components are added together. It is a vector kinetic field of stress energy, usually produced in periodic waves from AC sources. This type is detected in Josephson Junctions, and represented in a number of patents.

When AC power supplies of sines and cosines are used to produce curl free Poynting vectors, the Poynting vector fields have amplitudes that are described by squares of sines and squares of cosines. In this case all that is required to average out the AC feature is to produce two or more generators operating 90 degrees out of phase. The power input continues to flow. In the past some researchers suggested that the power somehow went back into the generators. This was refuted by placing the generators far enough apart.

A third type of curl free vector field is described in frame dragging, and is best represented as one or more moving wave fronts of vacuum stress energy. Claims are made of this type detected in small displaced orbits of satellites in Earth orbits. Some researchers do nor agree, but this is predicted in General Relativity.

If kinetic energy is carried in a local stress energy wave, then a curl free momentum vector field is implied. There is discussion about whether or not this is a special case of frame dragging. If this type of vector field did not exist then there would be no mechanism for speed of light to be a limitation on travel of physical objects.

Do researchers have other examples of curl free vector fields?

How Many Types Of Curl Free Vector Fields Are There?