Note 61 — Chapter IX · SCIENTIFIC WORK.—ELECTRICAL THEORIES.
Reading edition
It is difficult to explain without analysis exactly what is measured by Maxwell’s Vector Potential. Its rate of change at any point of space measures the electromotive force at that point, so far as it is due to variations of the electric current in neighbouring conductors; the magnetic induction depends on the first differential coefficients of the components of the electro-tonic state; the electric current is related to their second differential coefficients in the same manner as the density of attracting matter is related to the potential it produces. In language which is now frequently used in mathematical physics, the electromotive force at a point due to magnetic induction is proportioned to the rate of change of the Vector Potential, the magnetic induction depends on the “curl” of the Vector Potential, while the electric current is measured by the “concentration” of the Vector Potential. From a knowledge of the Vector Potential these other quantities can be obtained by processes of differentiation.