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T1 Hall Probe System
13 Some background about magnetic measurements
13.1 Measures of Magnetic Field Strength
Hall probes measure the magnetic flux density (also called magnetic induction), but it is useful to
see how this is related to other measures of the magnetic field.
There is a field around a current carrying conductor or a permanent magnet that exerts a force on
other current carrying conductors, moving charged particles, and compass needles. The force is
proportional to a measure of the field called the magnetic flux density. This is measured in tesla
-2
-1
-1
-2
-1
(T), or kg m s
A
m
= kg s
A
in SI base units. One tesla is a high field by everyday
standards, and is typical of the field in the air gap of a particle beamline bending dipole
electromagnet. The old cgs unit is the Gauss, and this is still widely used.
4
1 T = 10
Gauss
1 T = 10 kGauss
The Earth's magnetic field is around 0.5 Gauss at the surface of the Earth, varying with location
from about 0.25 to 0.65 Gauss.
It is common to describe the resistance of an energetic charged particle to being deflected by a
magnetic field by its magnetic rigidity, measured in tesla meters (Tm). A one Tm beam in a one
T dipole field will bend with a radius of one meter. An example of a one Tm beam would be
46.75 MeV protons.
The magnetic flux Φ which gives rise to the magnetic flux density is measured in webers.
-2
1 T = 1 Wb m
8
The old cgs unit of magnetic flux is the maxwell, but this is rarely used (1 Wb = 10
Mx).
You can consider that the magnetic field arises from a magnetizing field, H, which is due to the
motion of charged particles, usually electrons. In the SI system H is measured in amp per meter.
A magnetizing field H produces a magnetic flux density
B = µH
-7
where µ is the permeability of the local medium. In vacuum the permeability µ
= 4π x 10
0
-1
henry m
. The permeabilities of other materials are expressed relative to this. In ferromagnetic
materials the relative permeability may be hundreds or thousands. Air has a relative
permeability of very nearly one, so when you measure the B field with the T-1 system, you also
-1
get the H field in A m
after division by µ
.
0
The old cgs unit for magnetizing field is the Oersted.
-1
1 Oe = 1000/4π A m
and in vacuum 1 Oe creates 1 Gauss.
T1 User Guide
T1_UG_210314
Page 32 of 42
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