T
HEORY
5-2
April 2000 Rosemount Analytical 245364-U
Model 755A Oxygen Analyzer
Shaded
Pole
Piece
Sphere
(Magnetic Susceptibility = k
o
)
F
k
Sample Gas
(Magnetic Susceptibility = k
)
Note:
As percentage of oxygen in sample gas increases,
displacement force (F
k
) increases.
body begins to rotate, the amounts of light becomes unequal, resulting in application
of an error signal to the input of the amplifier circuit. The resultant amplifier output
signal is routed through the current loop, thus creating the electromagnetic forces
required to restore the test body to null position.
M
AGNETIC
D
ISPLACEMENT
F
ORCE
Because the magnetic forces on the spherical ends of the test body are the basis of
the oxygen measurement, it is worthwhile to consider the force acting on one of these
spheres alone and to disregard, for the present, the remainder of the detector. A
small sphere suspended in a strong non-uniform magnetic field, Figure 5-1, is
subjected to a force proportional to the difference between the magnetic susceptibility
of this sphere and that of the surrounding gas.
Magnitude of the force is expressed by the following (simplified) equation:
F
k
= c (k - k
o
)
Where:
c = A function of the magnetic field strength and gradient
k = Magnetic susceptibility of the surrounding gas
k
o
= Magnetic susceptibility of the sphere
The forces exerted on the two spheres of the test body are thus a measure of the
magnetic susceptibility of the sample and, therefore, of its oxygen content.
F
IGURE
5-1. S
PHERICAL
B
ODY IN
N
ON
-U
NIFORM
M
AGNETIC
F
IELD
