User:Jake Mokris/Hall Effect

Apparatus

This is the apparatus section of my lab report; it details the problems I discovered while attempting to take data. <math> \section{Apparatus}

The Hall apparatus we used comprised several parts: an electromagnet; a power supply for the electromagnet; two Hall probes, one with a silver strip and one with a tungsten strip; a current supply for the Hall probes; a Tesla probe, to measure the field in the electromagnet; a teslameter to output the value of the magnetic field read by the Tesla probe; a microvoltmeter; and a LABVIEW program to read in the data. \subsection{Electromagnet} The electromagnet consists of two sets of coils, with 250 turns each, sitting on an iron yoke \cite{electromagnet}. Atop each side of the yoke, above each set of coils, is another iron block with a metal disk attached to one of its sides, to focus the magnetic field above the center of the yoke. Since these iron blocks are clamped, not fixed, to the yoke, it is possible to vary the distance between the two metal disks, which changes the magnetic field strength. The Hall probe is placed in this gap, with the sample metal directly in between the two metal disks.

The maximum sustainable current through the electromagnet coils is 5 A \cite{electromagnet}. Though we exceeded that value at times, we found that it was possible to achieve a magnetic field of 500 mT between the metal disks with current less than 5 A, while at the same time keeping the metal disks far enough away to fit the Hall probe and Tesla probe comfortably in between.

We also found that the magnetic field varies greatly with position in between the metal disks. The disks themselves have a diameter of about 5 cm; when separated by about 1 cm, with the value of the magnetic field at the center at $-469$ mT, we moved the Tesla probe 1 cm to the left and to the right of the center. The field varied from $-485$ mT to $-453$ mT. We found that this asymmetry is persistent: the magnetic field gets stronger as we move the Tesla probe one direction horizontally from the center and gets weaker as we move the probe the opposite direction from the center. And we observe such an asymmetry every time we take data. We did not attempt to figure out why this happened, or if the field was always stronger on the left side and weaker on the right, or the opposite. We assume that this has to do with the alignment of the metal disks. If the disks were not exactly parallel, then they would be closer on one side and farther on the other. That should produce the asymmetry we observed.

Finally, when we measured the magnetic field at the very edge of the metal disks, we found that the field strength is drastically higher there than in the center, by as much as 200 mT. We do not know why this would be the case, but we surmise that it has to do with the shape of the magnetic field at the edges. Also, this should not affect the experiment greatly, as these larger fields are highly localized at the edges: we see this effect only within a millimeter of the edges.

\subsection{Electromagnet Power Supply}

The dial on the power supply to the electromagnet sticks and does not turn properly. This made it difficult to change the magnetic field strength smoothly.

We attached a multimeter in series with the power supply and electromagnet to more accurately measure the current supplied to the magnet. We found that, even if the dial is set to one current, the current value decreases over time, with a characteristic time of about 5-10 minutes. The current might decrease by as much as 0.2 A over this time. We did not experiment with the behavior of the current over time at constant settings. We did see, however, that the magnetic field does not change in the proportion we expected in response to this decrease: it causes a decrease of at most 1 mT in the magnetic field.

We also observed that most of the increase in magnetic field strength occurs when we change the current from 0 A to about 5 A. Over that increase, the magnetic field changes from about 0 mT to about 500 mT. When we increase the current from 5 A to 10 A, the magnetic field changes from 500 A to 600 A at most. We suspect that this has to do with the magnetization of the iron yoke and bars.

\subsection{Hall Probes}

Two Hall probes were available to us: one with a silver sample, and one with a tungsten sample. The Hall probes consist of the sample attached to a metal plate, with several wires attached to the sample along with sockets for connection to the microvoltmeter and current supply.

In addition, each Hall probe has a dial to control the resistance between the connections for the microvoltmeter. We found that this dial is broken in both Hall probes. When we measured the resistance between the two connections, we found that the circuit is entirely broken at most positions of the dial. If the dial is turned all the way to the right, however, the circuit is complete. We left the dial in that position while taking data.

\subsection{Microvoltmeter, Teslameter, and LABVIEW}

The microvoltmeter, which reads the Hall voltage, and the teslameter, which displays the magnetic field strength detected by the Tesla probe, are both connected to a computer with LABVIEW. We used a LABVIEW program to read in the Hall voltage values and magnetic field values. The LABVIEW program we used reads data continuously for a controllable amount of time and outputs the mean and standard deviation on the data read. We do not know the sampling rate of the program, nor were we able to extract the raw data. And unfortunately, the LABVIEW program cannot read values scaled above 5.0 in its voltage axis. So if the microvoltmeter reading was above 5, the LABVIEW program thought the voltage was exactly 5.0, scaled down a number of orders of magnitude equal to the gain setting on the microvoltmeter. So we had to decrease the gain in order to take measurements, which I believe hurt our measurements.

As we took data, we found that the mean field value outputted by the program was, on average, 5 mT smaller than the value displayed on the teslameter. We also found that, at times, the voltage read by the microvoltmeter would not change, even if we changed the magnetic field strength by up to 500 mT. However, this problem did not occur when we held the magnetic field constant and varied the current through the sample. As a result of this observation, we have no explanation for the constant Hall voltage readings when varying the magnetic field strength. I suspect that either the microvoltmeter is malfunctioning, or we did not have the gain setting on the microvoltmeter high enough. But, as mentioned previously, if the gain is set too high, LABVIEW is unable to read the Hall voltage. </math>

Hall Probe Adjusting Knob

So, this is what's going on: the samples are attached to a plate that you insert in the magnet. You connect all the detectors to this plate. Now, at the top of the plate, there's a knob that's supposed to adjust the resistance of the circuit that connects to the sample (this is from the manual):

"Before exposing the Hall effect apparatus to the magnetic field, adjust the zero point: Apply a transverse current I of e.g. 10 A and set the indicator of the meter for measuring the Hall voltage UH to zero using the adjusting knob. If the display changes after switching off, switch the transverse current back on and repeat the zero-point adjustment."

It turns out that this knob doesn't work. Depending on the position of the knob, it is possible to break the circuit entirely, so that no current will flow through it. Prof. Marriage measured the resistance of the circuit while varying the position of this knob, and found that at certain positions the resistance was infinite. This is clearly bad, for if the circuit is broken, the measurements of the Hall voltage won't change. And this is precisely what I've seen several times while taking data: the reading on the microvoltmeter doesn't change, even if I alter the magnetic field significantly.

What to Do About This

Before you take any data, measure the resistance across the sockets to which you attach the microvoltmeter. Turn the resistance-adjusting knob so that the resistance of the circuit is not infinite; the resistance should be very small. Leave the knob in that position while you take data.