334 Prof. J. J. Thomson on 
of the point ; a moving pole in an electric field will be acted 
on by a force mF wv sin 0, where F is the electric force, v the 
velocity, and @ the angle between F and 1; the moving pole 
will exert a force upon the fixed charge. 
If pole and point move with the same velocity, AB will 
move parallel to itself; there will be no change in the 
moment of momentum and no forces on the pole or point. 
If we had any number of poles of strengths 1, m,...2n 
at the points A,, Ay,...A,, anda system of charges @, és, 
€3,...é, at By, B,,...B,, the distribution of momentum in 
the field has for its moment of momentum the resultant of 
moments of momenta Dm,é, acting along A, Tie 
The following results are often useful in calculating the 
moment of momentum due to distributions of electricity over 
the surfaces of spheres. 
The moment of momentum, due to a pole at A and a charge 
at B, contained within a sphere of radius * with its centre at 
2 
as if ris less than AB: while the 
moment of momentum outside a sphere of radius 7, when 7 
either A or B is {me 
. e < A 
is greater than AB, is 3 me — 
~ tot 
_ Let us suppose that the pole is shielded from the electric 
force due to the charge by being placed at the centre of a 
metal sphere ot radius a; then inside this sphere there is no 
electric force. If we calculate the moment of momentum in 
this case, taking into account the charge induced on the 
sphere round the pole, we shall find that it is equal to 
a 
me({ 1 am) 
AB being supposed greater than a; the axis of the moment 
is along AB. In this case the moment of momentum involves 
the distance between the pole and the point ; so that if we make 
the point move towards the pole, the moment of momentum in 
the field will change, the moment of momentum lost or gained 
by the field is gained or lost by the sphere, so that the sphere 
moves as if acted on by a couple Zp where I’ is the moment 
of momentum of the field. Using the value of I just found, 
we find that the couple on the sphere is 
2meV a* 
AS” 
where V is the velocity of the point along AB. The existence 
i ie i a ee a eee Li 
