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
Here we must remember that .
(A) Energy of Heaviside Ellipsoid. If we put = S and make S large we have
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
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. It follows from this
- ↑ 'Electrical Papers' vol. ii. p. 505.