Similarly the magnetic force parallel to the axis of
and the magnetic force parallel to vanishes. Thus the magnetic force is the same as that which would be produced by a current-element or , being the velocity of the sphere (see Proc. Math. Soc. xv. p. 214).
The magnetic force inside the sphere parallel to equals
Substituting the value for given by equation (7), this equals
or, taking the real part and writing for ,
The component parallel to is
and the -component vanishes. Thus the maximum magnetic force inside the sphere is
If is very small, this is very small compared with the force outside the sphere. If the velocity is uniform, , and therefore , and the magnetic force inside the sphere vanishes. When there is no magnetic force inside the sphere its energy and the force acting upon it have the values assigned to them by Mr. Heaviside.
Let us next take the case where is small and large: in this case and have the same values as before, so that the magnetic force due to the moving sphere is the same.