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I am currently studying a eddy current disk break and came across this promising paper (PDF, princeton.edu) from 1942.

However, in the first formula a suspicious $4\pi$ appears before the current $U(x,y),$ stating

Let the eddy currents be confined to a finite region of the sheet which may or may not extend to infinity, and let us define the stream function $U(x,y)$ at any point in the sheet to be the current flowing through any cross section of the sheet extending from $P$ to its edge. The line integral of $\mathbf B$ or $\mathbf H$ over the closed path that bounds this section equals $4\pi U.$ From symmetry the contribution from the upper and lower halves of the path is the same so we may write $$\begin{align} 4\pi U = \oint \mathbf B\cdot \mathbf{ds} &= \pm 2 \int_x^\infty B_x~dx \\ &=\pm 2 \int_y^\infty B_y~dy\end{align}$$ where the choice of sign depends on the side of the sheet chosen for the integration.

How can this be explained?

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  • $\begingroup$ Can you restate the formula here and provide context? The link might not work for future visitors. $\endgroup$ – The Photon Mar 19 '19 at 21:01
  • $\begingroup$ @ThePhoton added. $\endgroup$ – CR Drost Mar 19 '19 at 21:28
  • $\begingroup$ I retract my earlier comment: while the equation $\nabla \times E = -\dot B' - \dot B$ suggests from its lack of $c^{-1}$ that these are not CGS units, the author explicitly mentions on the last page gauss and dyne-cm units, suggesting a preference for such Gaussian units. $\endgroup$ – CR Drost Mar 19 '19 at 21:58

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