hall eff martin

The Hall EffectAs 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.

Fig 1

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

. (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,

(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

. (3)

Current equals

(4)

where A is the area of the side of the slab. Hence,

, (5)

By plugging (5) into (4), and using (4) in (3), we find

. (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 determine the magnetic field produced

1. Experiment handout for Hall effect, Physics 616, The Ohio State University 1

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

Voltage vs. variable magnetic field times current.

Fig 3

Voltage vs. variable current times magnetic field.

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.

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

(7)for a non-ideal solenoid.


Fig 4

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

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.

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.


hall eff martin

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