MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
709 
Motion of a Charge in a Uniform Magnetic Field. 
20. It has ofien been thought that some of the peculiar effects produced by a 
magnet upon vacuum tube discharges are to be explained by supposing that the dis¬ 
charge consists of charged particles Hung off with considerable velocities from the 
negative electrode, and that each charged particle in motion is acted on mechanically 
by the magnetic field. It will, therefore, be of some interest to write down the forces 
experienced by a charged particle when moving through a uniform magnetic field. 
The system which produces the field may be in motion, but it is supposed to be a 
purely magnetic system, i.e., one in which F = 0, so that a charged particle moving 
with the system experiences no force. The velocity of this system will be supposed 
to be u parallel to the axis of x. The moving charge q is supposed to have a velocity 
w, whose components are w l} iv. 2 , iv 3 . Then, if P denote the mechanical force on q, we 
have, by (65), 
P= q( E + zrVwH).(88). 
But the state of the field must be determined experimentally by estimating the 
force on a unit magnetic pole, which we shall suppose is moving with the magnetic 
system. This is exactly what we find when we make experiments to find the intensity 
of any magnetic field by means of a magnet, for this field and the magnet are both 
carried along by the rapid motion of the Earth. It is, in fact, R, which we measure, 
and not H. We must, therefore, determine E and H in terms of It, the only quantity 
which we can observe. This has already been done in equations (76) and (77), where 
we have now to put F = 0, so that, 
Ej = 0, E, = Bo, E 3 = - ^ R 2 , 
H, = R„ H, = 1 R.„ H 3 = - R 3 . 
u a 
Expanding P into its three components and substituting the above values of E and 
H, we find 
P J = /x 2 i^R 3 -^R 2 ‘ 
a 
u — w 
1 R, 
p 3 = gq jnvRa + 
P 3 = ftJ |-'-^R 3 - s » 3 R 1 } 
.(89). 
When the charge and the magnetic system are moving together so that iv l = u, 
w 2 — w z — 0, then P vanishes. There is thus no force on a charged body when it is 
placed near a magnet, and both are carried through the ether by the motion of the 
earth. 
