Momentum in the Electric Field. 347 
momentum in the field has a finite resultant passing through 
the fixed electrified point. For consider a magnetized element 
AB (fig. 3) and an electrified point at P, then if m is the 
Fig. 3. 
P 
B 
streneth of the pole at A, —m at B, the momentum in the 
field calculated on the assumption that the magnetic force is 
equal to the magnetic induction at every point in the field, 
is made up of a moment of momentum em along AP anda 
moment of momentum —em along BP. The resultant of 
emAB sin 0 
OP 
to OP, O being the middle point of AB and @ the angle 
AOP. This moment of momentum is equivalent to a 
momentum oe aed through P at right angles to 
the plane of the paper downwards and a momentum 
mAB si 
ao through O at right angles to the plane of the 
these is a moment of momentum at right angles 
paper upwards. In the magnet, however, the magnetic 
induction is not equal to the magnetic force, so to get the 
momentum we must add to the preceding momentum a 
momentum equal to (difference between magnetic induction 
and magnetic force in the magnet) x (electric polarization at 
right angles to AB) x volume of magnet. The direction 
of this momentum is at right angles to the plane of the paper 
downwards. Now the difference between magnetic induction 
and magnetic force =47I, where I is the intensity of 
magnetization, the polarization at right angles to AB is 
ae Bin? ; hence the additional momentum is pan? (volume 
Ag OP? 
OR? 
of magnet), but I x (volume of magnet)=m.AB. Hence we 
see that this momentum just balances that acting through 
