22
2.
THE MASS OF THE ELECTRON
.
-
region BC, as indicated by the dots, the spot of light is deected
to S'.
Thus the rays are bent into a circular path of rad1us r
centimeters while moving through the eld BC and thereafter
travel in a straight line.
_
—[= +ë V
'
'P
"
'
'
,—
.
—"
B
@
r"”””
s
…….\_ f
.
_
Illlllllllh—‘l
.
rÿ/r
-
9
Fig. 2—2. ]. ]. Thomson’s method of measuring e/m and 0.
Consider a space one centimeter in cross-section and 0 centi- '
_
meters long which contains n electrons per cubic centimeter, each
charge &. Then ne is the charge per cubic centimeter.
If a is
'
the velocity with which the electrons are moving, (ne)v is the
_
quantity of electricity which Will pass a given point in one second.
,
-
Thus a stream of electrons is equivalent to a current z' = mb}
-Now, by denition of the electromagnetic unit of current, the
magnetic force on the current is Hi and hence on each electron is
This inward or centripetal force is c0unterbalanced by the
outward centrifugal force mv2/r, so that the electron travels ina '
circular path of radius r as long as it remains in the magnetic
'
.
eld.
Thus We may write
-
.
_
H6’0 = mvz/r,.
or
e/m_ = v/Hr.
'
(25—1_)
'
The magnetic eld intensity H can be calculated from the magni—
_
tude of the current used to produce it and the dimensions of the
:
coil, or it may be measured directly with.
ux-meter.
The,
Ÿ
radius r may be calculated from the dimensions of the apparatus
and the deection D (see gure 2—2). ' Thus '
_
,
_.
_
-
’ _*
tan 9 : l/r = D/VD2 + L2,
r = [V1 + L2/D2. =(2—2). .