Hall Effect in a Conductor due to its Own Magnetic Field

If there is at each point in a conductor an electric intensity proportional to the vector product of the magnetic field and current density, there should be a difference of potential between points at different distances from the axis of a cylindrical conductor carrying a current. Rather than attempt to measure this, a qualitative confirmation of the existence of the effect was sought by use of a cylindrical specimen of bismuth having a long section of small diameter (3 to 4.8 mm) between two larger end sections (12.5 mm). When 60 cycle alternating current was sent through the specimen, the mean potential differences between the surface of the small section at the point $M$ and two points $A$ and $B$ on the surface of the larger sections at each end, was measured by means of a tuned electro-dynamometer connected from $M$ to the balance point on a semi-circular conductor connecting $A$ and $B$, at which the 60 cycle potential differences were balanced out. This Hall effect has a double frequency because it does not reverse with the current. The resulting deflections were from.1 to.3 times the theoretical upper limit, therefore in good qualitative agreement. That they were not due to thermo-electric effects was proved by the absence of the effect when an alloy with zero Hall coefficient was substituted, as well as by other tests. It is concluded that the Hall effect is always present in wires carrying currents and should cause a slight increase of resistance at high current densities.