**Context**:

Smudge's thread on the Marinov motor had been very instructive in leading us to questions about the vector potential, for example about a possible motor without an active magnetic field or about a possible induction by a spatial rather than temporal gradient of the vector potential.

The vector potential A is the equivalent for the magnetic field of what the (scalar) potential is for the electric field. The vector potential has its lines along the currents. If the conductor is linear, the lines will be oriented along a tube around the current. If it is a coil, they will be circles around it which, unlike the magnetic field confined to the interior of the coil, are established in all continuity from the interior to the exterior of a coil until infinity.

A temporal variation of this field is seen as an electric field E, which is another way of seeing the induction field created by a variation of magnetic field.

**E=-∂A/∂t**.

**The idea**:

Starting from this, we can re-write

**E = - ∂A/∂x * ∂x/∂t = - v * ∂A/∂x**. From this equation, we can derive that, with respect to an observer linked to the source of the vector potential, a charge moving at speed v along the x axis, will see an electric field proportional to the spatial gradient along x, of the vector potential. This is true whatever the space coordinate x, y or z. We have just assumed here that the gradient of A and the motion of the charge are only along x.

The question remains how one can verify this experimentally, namely to induce a current from a spatial gradient of the potential vector, which would be a new form of generator or transformer.

Smudge has proposed a method in his thread

"Generator using a superconductor". Here is another one that I propose.

The potential vector is established along a current and depends on it, so we would need a circuit with a non constant current along the circuit. By "non-constant", we do not mean a current which varies in time, but a current which at a given moment, is not the same everywhere along the circuit, which in opposition to Kirchhoff's law seems difficult to obtain in the regime of quasi-stationary states.