Letter | Published:

A Comprehensive Fundamental Electrical Formula

Nature volume 143, page 601 (08 April 1939) | Download Citation



MR. DUNTON'S measurements do not in any way affect the validity either of my equation, the Biot-Savart law, Faraday's law of electromagnetic induction, or the magnetic flux-cutting equation. His error lies in assuming that it is only the magnetic field of the lower fixed portion M1ADM2 of the accompanying circuit which produces a force on the conductor BC; whereas the only part of the magnetic field produced by the whole circuit which does not produce a force on BC is that due to BC itself. If for simplicity we consider a very long narrow rectangular loop of breadth b and conductor radius a, the magnetic force at any distance x from AB and remote from BC or AD is H = 2I/x + 2I/(b–x), and hence if the length of the loop is increased by the amount dy neglecting the internal magnetic field in the conductors. But the magnetic force at a corresponding point on BC is H′ = H/2, and the force on BC or on AD is therefore which is Maxwell's formula, with which Mr. Dunton's measurements agreed. He ought actually to have observed a somewhat greater force due to the pressure on the ends of the conductors caused by the constricting effect of the current in the mercury (the ‘pinch phenomenon’ of Carl Hering), which is covered by the same argument; but the above is sufficient to show that his supposed discrepancy has no foundation.

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