# Origin of Textbook Argument for Displacement Current as Generalization of Ampere's Law

I was wondering where in the literature the standard textbook argument (appearing in Young and Freedman and Purcell and Morin, for example) for displacement current first appears. It seems especially odd to me that Maxwell didn't include it in either his Treatise or research papers seeing as he certainly knew of Stoke's Theorem, Ampere's Law and capacitors

From this good review:

1. Ricardo Karam, Debora Coimbra, and Maurício Pietrocola, “Comparing Teaching Approaches About Maxwell’s Displacement Current,” Science & Education 23, no. 8 (August 1, 2014): 1637–61, doi:10.1007/s11191-013-9624-3,

on p. 1646 they quote this passage of Maxwell's Treatise on Electricity & Magnetism (vol. 2, pp. 142-144):

The current produces magnetic phenomena in its neighborhood. If any closed curve be drawn, and the line-integral of the magnetic force taken completely round it, then, if the closed curve is not linked with the circuit, the line-integral is zero, but if it is linked with the circuit, so that the current i flows through the closed curve, the line-integral is 4πi […] Note—The line-integral 4πi depends solely on the quantity of the current, and not on any other thing whatever. It does not depend on the nature of the conductor through which the current is passing, as, for instance, whether it be a metal or an electrolyte, or an imperfect conductor. We have reason for believing that even when there is no proper conduction, but merely a variation of electric displacement, as in the glass of a Leyden jar during charge or discharge, the magnetic effect of the electric movement is precisely the same.

(their emphasis)

By "in the glass of a Leyden jar," Maxwell means "in the space between the plates of a capacitor." (Leyden jars were an early form of a capacitor.)

They also note (ibid. fn12):

The first record of such experiment[s "that aimed at providing evidence for the existence of the displacement current by measuring the magnetic effects between the plates of a charging (or discharging) capacitor"] goes back to 1899 in the report "On the Magnetic Action of Displacement-currents in a Dielectric" written by Silvanus P. Thomson.

As an aside, Ampère never wrote down "Ampère's law", even the form without Maxwell's added displacement current term, as Ampère never dealt with the field concept. Ampère's force law4th Maxwell equation called "Ampère's" circuital law.