Momentum in the Electric Field. 343 
motion the force on the electrified plates will not alter until 
the pulse reaches them, and so will continue to pass through 
OQ. The force on the point will, however, pass through 0/. 
Thus we get a couple whose moment is XeOO! or Xewt, 7. e. 
the couple required to keep the moment of momentum of the 
system constant. 
Momentum when a charged point at rest is placed in the 
field due to a moving charged particle.—If the external electro- 
static field in the last example had not been uniform but that 
due, say, to a charged particle at P, then we should have 
found that the momentum as well as the moment of momen- 
tum in the field would change as the pulse spreads out. In 
this case the force acting on the moving particle when it is 
at O’ is ee’/O’P?, and acts along O’P, while the force acting 
on P is ee’/OP? along OP, O being the initial position of O’. 
In this case, since ‘OP is not in general equal to O/P the 
forces on Q/ and P are not equal in magnitude, so that there 
is a resultant force acting on the system. 
If e is the charge on the moving point O, u, v, w the 
components of its velocity, then a, 8, y the components of 
the magnetic force produced by it at a point P whose co- 
ordinates are «, y, z, are given by the equations 
ae al a i! 
a=e(e er ys) 
dil d 1 
BN dar ee) 
ee LSS id 1 
y=e(" dyr "da? 
where * is the distance of P from’O. If Q is the position 
of a charge e’ at rest, then 7, g, h, the components of the 
electric polarization at P due to this charge, are given by the 
equations 
egy ee ge at 
TONGS ee eee dy rv’ Ag dz r” 
r' being equal to PQ. 
U, the x component of the momentum in the field, is 
given by the equation 
Ba e\\) to eerie | 
ed patyeit /, 41 
ee aon, | dy r 
a1. 
Be tea pe ave 
2A 2 
