Page:PoyntingTransfer.djvu/17

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from some fixed plane by , the line integral of the M.I. is , while the current, being an alteration of displacement, is

Therefore

(2)

But since the displacement is propagated unchanged with velocity , the displacement now at a given point will alter in time to the displacement now a distance behind, where .

Therefore

(3)

Substituting in (2)

whence

(4)

the function of the time being zero, since and are zero together in the parts which the wave has not yet reached.

If we take the line-integral of the E.M.I. round a face perpendicular to the M.I. and equate this to the decrease of magnetic induction through the face, we obtain similarly

(5)

It may be noticed that the product of (4) and (5) at once gives the value of , for dividing out we obtain

or

But using one of these equations alone, say (4), and substituting in (1) K for and dividing by , we have

or

whence