Page:SearleEllipsoid.djvu/12

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When is large the quantity in [ ]

vanishing when .

Thus, making use of we have for the magnetic energy

.

Now by (17) we have at the surface of the ellipsoid

.

Hence the total electromagnetic energy of the ellipsoid is

. (23)

Here we must remember that .

(A) Energy of Heaviside Ellipsoid. If we put = S and make S large we have

(24)

This corresponds to the Heaviside ellipsoid, for when , . The energy of the same ellipsoid at rest is

.

(B) Energy of a Sphere. Putting we have , and thus

. (25)

If is small compared with we have

.

It will be found that as far as the magnetic energy is

as has been found by Mr. Heaviside.[1] It follows from this

  1. 'Electrical Papers' vol. ii. p. 505.