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5.3 Calculating e/m und v
5.3.1 By means of magnetic deflection
Set up the experiment as in Fig 2.
The velocity is dependent on the anode voltage
U
such that:
A
e
2
v
U
A
m
Solving equations 1 and 3 simultaneous gives the
following expression for the specific charge e/m:
e
2
U
A
2
m
B
r
U
can be measured directly, B and r can be de-
A
termined experimentally.
5.3.1.1 Determining r
The radius of curvature r is obtained geometri-
cally as in Fig. 1:
2
2
r
x
r
y
so that:
2
2
x
y
r
2
y
5.3.1.2 Calculating B
The magnetic flux B of a magnetic field generated
by the Helmholtz coils in Helmholtz geometry and
the coil current I can be calculated:
3
μ
4
2
0
B
5
R
where k = in good approximation 4,2 mT/A
with n = 320 (windings) and R = 68 mm (coil ra-
dius).
(3)
(4)
2
(5)
n
I
k
I
(6)
5.3.2 By means of electric deflection
Set up the experiment as in Fig 3.
e/m can be calculated from equation 2:
2
e
2
y
v
2
m
E
x
U
P
where
E
d
with U
= deflector plate voltage and d = plate
P
spacing.
5.3.3 By means of field compensation
Set up the experiment as in Fig 4.
Turn on the high-tension power supply units
and deflect the beam electrically.
Energise the Helmholtz coils and adjust the
voltage in such a way that the magnetic field
compensates the electric field and the beam
is no longer deflected.
The magnetic field compensates the deflection of
the electron beam caused by the electric field:
e
E
e
v
The velocity v can be calculated:
E
v
B
U
P
where
E
. For the calculation of B refer to
d
point 5.3.1.2.
The specific charge e/m can be calculated:
e
1
m
2
U
A
3
(7
B
(8)
2
E
(9)
B
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