The Hall Effect
As preformed by Brian D’Angelo and Jesse Martin
Written by Jesse Martin
In this report, the Hall effect is verified. It is demonstrated that this effect is linear with
regards to the current and the magnetic field applied to the Hall substance. The magnetic
field of a solenoid is measured.
The Hall effect was discovered in 1879
by the physicist whose name it now
bears: Edwin Hall. Hall discovered this
galanomagnetic effect as a graduate
student at John Hopkins University.
As a “slab” of some substance has a
current passed through it and is
simultaneously exposed to a magnetic
field, a voltage will build up across the
sides parallel to the current flow.

V
FE  qE  q H
w
(2)
until the two forces equalize. Here, w is
the width of the slab, or the separation of
the charges, and VH is the Hall voltage
that is measured across the slab. Once
the two forces equalize, we get
qvB  q
Fig 1
VH
.
w
(3)
Current equals
I  qnvA
(4)
where A is the area of the side of the slab.
Hence,
A  wt ,
A slab of material in a magnetic field
with an applied current.
The moving charges will feel a Lorentz
force as they pass through the magnetic
field. This force is given by

 
FB  qv  B .
(1)
This will separate opposite charges to
opposite edges, and it is this separation
that will produce the voltage. From the
voltage, a force in opposition to the
Lorentz force will build. This force will
behave thusly,
(5)
By plugging (5) into (4), and using (4) in
(3), we find
VH  RH
IB
.
t
(6)
RH is known as the Hall coefficient and
has units m3/coul, I is the current being
passed through the substance, and t is the
thickness of the slab1.
Before data could be taken, the Hall
probe had to be calibrated, and the
nature of the Hall effect verified. A
commercial gauss meter was used to
1. Experiment handout for Hall effect, Physics 616, The Ohio State University
1
determine the magnetic field produced
by a variable field magnet. This magnet
was then used to calibrate the Hall probe
by charting the effects of varying current
or magnetic field.
Fig 2
Variable B field
0.12
0.1
V(300.5 mA)
0.08
0.06
0.04
0.02
0
0
100
200
300
400
500
600
700
B* 300.5 mA
Voltage vs. variable magnetic field times
current.
Fig 3
Once the probe was calibrated, the
magnetic field of a solenoid was
measured. Two solenoids were placed
end to end to form one long solenoid
with a length of 31.0 ± 0.5 cm. The
probe was placed in between the two
solenoids, and the field was measured.
From the field, the number of loops that
made up the solenoid was estimated to
be 1054 ± 78 by using the formula for
the magnetic field inside an ideal
solenoid. The true number of loops was
counted to be 1090. As can be seen, the
calculated number is consistent within
uncertainty.
Finally, data was taken outside of the
solenoid along the axis. This was done
with the Hall probe and a commercial
gauss meter, different from the one used
to calibrate the Hall probe. The
expected magnetic field of the solenoid
was also calculated using
Variable current
0.1
0.08
0.06
V(1.25 kG)
As can be seen from figure 2 and 3, the
data exhibits a linear region at low
currents and low magnetic fields, and
then curves off at increasing current and
magnetic fields. It seems that the Hall
coefficient changes as I and B reach a
certain threshold. The Hall coefficient
was determined by taking the data from
just the linear region and, when divided
by the thickness of the sample, was
determined to be 0.000170 ± 0.000007
m2/coul.
0.04

dL
 0 IN 
2
B

2
2L 
2
L
 d
R
2

0.02

0
-0.02
-100
0
100
200
300
400
Current * 1.25 kG
500

600


2

2
d  L  R2 
2

(7)
d L


for a non-ideal solenoid.
Voltage vs. variable current times
magnetic field.
2
Fig 4
the Hall probe was centered on the axis
and whether or not it traveled perfectly
along the axis. This would cause a shift
in the magnetic field that would help
explain the shift in the graph. If the
probe did not travel perfectly alone the
axis, then it would not be as far from the
solenoid as measured. It would be offset
by some angle theta, which would
decrease the distance and increase the
field measurement. This would not be a
huge offset, but in this region even a
small offset will produce a large
difference.
B (Hall Probe)
B (gauss meter)
B (expected)
Data B2 Bm Bc
60
50
B (Hall Probe)
40
30
20
10
0
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
x
B field as measured by the Hall probe
and gauss meter with the expected field.
As can be seen, all the graphs have the
same general shape. The offset suggests
that there is some systematic error
involved. Let’s consider each curve one
at a time.
First, the curve generated by the Hall
probe. It seems to be leveling off as it
approaches a magnetic field of 10 G. It
has been suggested that it is not an ideal
Hall probe and that it may have some
inherent systematic error. The device
was never checked for a magnetic field
of zero during calibration as the variable
field magnet did not go to zero, so it is
possible that as long as a current is
flowing through it, even if it is not
exposed to a magnetic field, some Hall
voltage will be measured, resulting in a
pseudo-magnetic field. The earth’s
magnetic field may have some
contribution, but it would only be on the
scale of 4 Gauss. However, when we
decrease the curve by 4 Gauss, it does
appear that it is consistent with the
expected curve within errors. Another
systematic error would be whether or not
If we consider the curve produced by the
gauss probe, we can assume the same
axial movement difficulties. Other than
the inherent uncertainty of the gauss
meter, there is nothing else to consider
for this curve, as the Earth’s magnetic
field was taken into consideration when
calibrating the meter.
The finally curve is the expected curve.
The primary uncertainties are systematic
in nature. They are uncertainty in length
of the solenoid, and in the radius, as the
radius had some thickness to it, and the
equation used assumed perfectly thin
walls.
In conclusion, the Hall effect was
verified. As long as the magnetic field
and the current stayed below some
threshold, there was a linear relationship
between the voltage measured, and the
current and B field applied. The
characteristics of the magnetic field
produced by a non-ideal solenoid were
also measured. The magnetic field was
found to fall off quadraticly in
accordance with theory and the number
of turns in the solenoid was predicted
with in errors.
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