Momentum in the Electric Field. 341 
are respectively :— 
Hew (x? +77) Hew yz 
0, doV6S ? > ArVS Pr * 
Integrating through the shell the components parallel to « 
and 2 vanish, and that parallel to y becomes 
2 Hew 
Eee 
where OA is the inner radius of the sphere, and is equal 
to Vt. Hence the momentum in the shell parallel to y is 
equal to 
? 
SEE. 
3 
The electrostatic field inside the shell is at the time ¢ that 
arising from a point O’ which is not at the centre of the 
shell, but such that OO!=wt. Calculating the momentum due 
to this field and the external magnetic force H, we find that 
Is : HeOQO’ ae Hewt ; hence the total momentum on the 
a 
shell and inside it is 
Heuwt. 
Thus on the hypothesis that the pulse formed in the 
magnetic field is the same as that formed when the external 
magnetic field is absent, we conclude that the momentum in 
the field at right angles to the direction of the magnetic 
force, and also to the direction of motion of the charged 
particle, is increasing at the rate Hew. By the principle of the 
conservation of momentum, the material system, 7. e. the 
charged body and the magnet, must be losing momentum at 
that rate, 2. e. they must be acted on by a force parallel to y 
equal to —Hew. Now the charged particle is moving ina 
magnetic field, and so is acted on by a force parallel to y 
equal to —Hew; while, since the wave of magnetic force has 
not yet reached the magnets, the latter do not experience any 
mechanical force. Thus the whole force acting on the system 
is such as to give to the system the momentum lost by the 
field. Thus the view that the wave of magnetic and electric 
force produced by the sudden starting of the charged point 
is not affected by the magnetic field is consistent with the 
principle of the Conservation of Momentum. We notice 
that the momentum arising from the external field vanishes 
when ¢=0. Thus the momentum at that time is not affected 
Phil. Mag. 8. 6. Vol. 8. No. 45. Sept. 1904. 2 A 
