Rosemount 755, Instruction Manual

Page: 55 / 94

I
NSTRUMENT
T
HEORY
748183-H
5-3
Rosemount Analytical
December 1997
5.1.1 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 5-2, 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:
Fk = c (k - ko)
Where:
c = A function of the magnetic field strength and gradient
k = Magnetic susceptibility of the surrounding gas
ko = Magnetic susceptibility of the sphere
The forces exerted on 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
5-2. S
PHERICAL
B
ODY IN
N
ON
-U
NIFORM
M
AGNETIC
F
IELD
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.