Momentum in the Electrie Field. ao0 
of this couple would, on the more usual way of regarding the 
phenomenon, be explained by noticing that when the charged 
point moves towards or away from the sphere the distribution 
of electricity over the surface of the sphere changes. There is 
thus a movement of electricity over the surface of the sphere 
constituting a system of electric currents, and the mecha- 
nical forces arising from the action on these currents of the 
magnetic field due to the pole at the centre gives rise to the 
couple whose moment we have just calculated. 
If we consider the term em in the expression for T' we get 
the same forces on the pole and the point as if the shielding 
ma? 
sphere round the pole were absent, while the term —_ 
easily be seen to give rise to a couple acting on the system 
consisting of the pole and sphere whose components parallel 
to the axes of w, y, z are respectively 
2 2 2 
ema? {uF z aft “a4 
da? r * a dy r dedz r 
Be @& 1 + & +w oi 
cues ear dy r aa yy? dydzr J” 
may 
é 2 ? = ob ee ee 
toy (eer, i ” dy ae ¥ dr J’ 
where w, y, z are the coordinates of B, r=AB, u, v, w are 
the components of the velocity of B. We see from this 
expression that the axis of the couple on the sphere is parallel 
to the magnetic force at A due to a doublet at B magnetized 
parallel to the direction of motion of B. If the moment of 
this doublet is equal to the velocity of B, then if H is the 
force at A due to this doublet, the couple on the sphere has 
its axis parallel to H and its moment equal to Hema’. 
Let us suppose that, instead of a charged point we have a 
uniformly electrified spherical surface. Let e be the charge on 
the surface, a the radius of the sphere, B its centre. Then 
if the pole is at B, the moment of momentum about AB of 
the field is > 
Bi ea 
em ( 3 AB? . 
Here, as in the last case, we have, in addition to the forces 
which would act on a charge e placed at the centre, and on 
