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⋅
2
U
e
=
A
(
)
⋅
2
m
B
r
U
can be measured directly, B and r can be deter-
A
mined experimentally.
5.3.1.1 Determining r
The radius of curvature r is obtained geometrically as
in Fig. 1:
2
r
=
x
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
⎛
⎞
4
2
=
⋅
⎜
⎟
B
⎝
⎠
5
where k = in good approximation 4,2 mT/A
with n = 320 (windings) and R = 68 mm (coil radius).
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
(4)
(
)
2
2
+
r
−
y
(5)
μ
⋅
n
⋅
=
⋅
0
I
k
I
(6)
R
(7
Fig. 1 Determining r
U
=
P
where
E
d
with U
= deflector plate voltage and d = plate spac-
P
ing.
5.4 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 volt-
age in such a way that the magnetic field com-
pensates 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
The velocity v can be calculated:
E
v =
B
U
=
P
where
E
. For the calculation of B refer to point
d
5.3.1.2.
The specific charge e/m can be calculated:
⎛
e
1
=
⋅
⎜
⋅
⎝
m
2
U
A
3
⋅
=
⋅
⋅
E
e
v
B
(8)
2
⎞
E
⎟
(9)
⎠
B
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