Establishing a Hall Potential in Silver via an Orthogonal Magnetic Field to Deduce the

Density of Accumulated Negatively Charged Particles

Created by Brian Hallee

Partnered by Joseph Oxenham

Performed October 29, 2010

Historical Background

The Hall Effect is known to be one of the most precise and defining physical phenomena

to ever be discovered. Its discoverer, of whom the effect has since been named after, was

Edwin Hall who happened across it while performing experimental work for his doctoral

dissertation in 1879.1 Over the course of his doctoral studies, which naturally took place in the

realm of physics, Hall experimented with small metal leaflets by passing a current through their

length and a magnetic field through their face (orthogonally). After subsequently tapping off

the leafs at various points down their length with a voltmeter, he noticed that in a short

amount of time that the presence of a magnetic field would cause a very small potential

difference from top-to-bottom. This harmoniously further united electric current with magnetic

fields, and lead 19th century physicists further down the road to understanding the quantum

mechanical atom.2 An interesting setback to the results of this experiment was the fact that the

electron was still a mystery at this point in time. J.J. Thompson of Cambridge University would

not go on to rigorously prove its existence another two decades. Thus, Hall and others had to

await the formation of quantum mechanics in order to fully conceptualize his discovery. While

the significance of this seemingly trivial electric potential will be developed and explained fully

in the theory section, it is worth noting that Hall’s discovery has spawned several related

discoveries on the quantum scale.3 These new quantum-based Hall effects have not only found

their way into many modern applications you likely use every day, they have also helped to

narrow down physical constants (i.e. the fine structure constant) to one part in a billion.4 Only

three decades ago was the Hall Effect generalized to the quantum scale. The “integer”

quantum hall effect was first predicted by three physicists in 1975 who, in turn, doubted their

Page | 2

own calculations. Nonetheless, five years later, a team led by Dr. Klaus von Klitzing discovered

that the Hall conductivity increased by, what physicists now grant as, exact integers. 5

Considering this is rather beyond the scope of this report, I ask you to treat as an axiom the fact

that this effect has helped narrow the value of h

e2 and the value of the “fine structure constant”

α . (A value of utmost importance in quantum electrodynamics) The fraction h

e2 has since been

bestowed the term “von Klitzing Constant” in his honor, and in 1985 the quantum Hall effect

had become relevant enough to grant him the Nobel Prize in Physics of that year.6 With the

advancement of integrated circuit technology, the Hall Effect has found useful application in the

form of Hall Probes or Hall Sensors. These devices often serve as miniature magnetometers

mostly for magnetic field detection and flux leakage measuring. Hall Probes require integrated

circuit amplifiers for the reason that, as we will observe in the following sections, Hall voltage

levels are extraordinarily small and require large sophisticated voltmeters for accurate

measurements at this scale. Typically, they find a home in all types of sensing equipment such

as speed, pressure, current, or fluid-flow sensing. They are also likely to be paired up with a

potentiometer for applications that require a switch to be robust (eg. electric guns).7 While one

would be inclined to believe that physicists would have, more or less, “closed the book” on the

Hall Effect by stretching and generalizing it as far as is physically feasible over the past 100

years, this is not the case. Currently, heavy research is involved in understanding the physics

behind the fractional quantum Hall Effect; discovered in 1982. As common sense would

suggest, the discovery of this phenomenon stemmed from the observations of Hall steps with

fractional quantum numbers. The brunt of the understanding of this occurrence comes from

Page | 3

Figure 1: A semiconductor experiencing the Hall Effect

From: Hyperphysics – Hall Effect2

the utilization of “wave-functions”. However, as this article undergoes construction, heavy

research remains in the realm of “quasi-particles” and their atypical fractional charge.

Theoretical Basis

Fortunately, as scientists of the

twenty-first century, we are able to

apply the electron and proton to

our conceptual examples to fully

grasp the phenomenon and apply

mathematics to it. The derivation

of the hall voltage is relatively simple

an only requires a firm understanding

of current, magnetic force, and Newton’s second law. We will refer to figure 1 quite frequently,

and it is only fitting that we inform you of the meaning behind the variables it contains at the

start.

I = The current passing through the semiconductor (Natural convention calls for this to designate positive charge movement (protons) {Depicted in the diagram} We will observe shortly that we are only concerned with electron movement in this experiment.Fm = The magnetic force exerted on the moving charge carriers B = The magnetic fielddT = The thickness of the plate (In our derivation, we will simply designate this as T)D = The height of the plateFE = The electric forceVH = The Hall Voltage. (To differentiate this from regular potential and velocity, we will use Hv)

If we further bestow another variable to the figure, dX (An infinitesimally small length spanning

the “height” of the block), we can state that a charge dQ moves through the length dX over a

Page | 4

time dt. Unfortunately for Hall, this is where his toils would have ended, as we are ready to

apply the notion of a “charged particle”, or electron, to the derivation. At this point, the

volume dX contains an amount of charge dQ, or the number of individual charged particles

times the volume they occupy. Thus,

Charge∈dX=dQ=ndV (eqn. 1)

We can infer from figure one that the volume dV is equal to T*D*dX. Therefore,

dQ=nTD∗dX (eqn. 2)

If we divide equation 2 by the differential time we spoke of earlier, we obtain:

dQdt

=nTD dXdt→I=nTDvd (eqn. 3)

We utilized the fact that charge per-unit time is current, and distance per-unit time is velocity

to achieve equation 3. The subscript d for velocity denotes the “drift” nature of this movement.

Barring unnecessary electrodynamics, the drift velocity arises from the mostly random motion

of electrons. Although we tend to believe that all electrical phenomena operate at relativistic

speeds, this is simply not the case for mean electron movement in a wire. When an electron

field is present, they will tend to drift, on the order of 10-4m/s, towards their destination due to

the large amount “roadblocks” (nuclei, inter-molecular forces, etc.) they must overcome. 8 This

drift velocity will come in handy as our derivation progresses. Thus we re-write equation 3 as

follows:

vd=I

nTD (eqn. 4)

Page | 5

Next, we consider the magnetic field and its effects on our stream of charged particles. The

general equation governing magnetic force on a charged system is written as follows:

FB=q∗v x B (eqn. 5)

Before we move any further, we must denote what charges are actually of focus in our

experiment. To solve this, we will treat as an axiom the fact that semi-conductors (such as

Silver, our metal of choice) allow for negative charge movement within their structure.9 In

layman’s terms, when a current develops in our sample, we can safely assume that electrons

are the cause of this, and they move in the opposite direction of standard convention. Thus,

when applying equation 5 both quantitatively and qualitatively, we must take into account the

negative charge attributed to electrons. We will begin with the qualitative argument to support

figure 1 and its, thus far, mysterious charge accumulations.

FB=−[ (−i )x (−k ) ]=+ j (eqn. 6)

Equation 6 is strictly concerned with the vector analysis of equation 5. It predicts that an

electron with velocity moving in the opposite direction of the current (denoted (-i)) acted upon

by a magnetic field perpendicular to its velocity (denoted (-k )) will be forced “upward” along

the height of the metal plate. By this reasoning, it seems as though in a short time negative

electrical charge will accumulate towards the top, and this is exactly what we observe

experimentally. In fact, this phenomenon naturally causes a net positive charge accumulation

on the bottom and, thus, a Hall Potential is born between the two. This is precisely what Dr.

Hall observed, and we will continue our quantitative derivation to arrive at a clean formula to

predict what this potential might be. Taking the absolute value of equation 5:

Page | 6

¿ FB∨¿ qvB=−evd B (eqn. 7)

Thus, we observe the drift velocity coming back into play, and we require one more observation

to tie it all together. Once the accumulations have settled down, a miniscule net electric field

develops between the positive end and the negative end. From introductory electrostatics, we

know:

FE=q∗E=−e∗E (eqn. 8)

Allotting enough time for the accumulations to reach equilibrium, (In reality, this takes only

seconds), we are able to apply Newton’s first law to the electric and magnetic forces:

FE=−FB (eqn. 9)

Therefore,

e E=e vd B (eqn. 10)

Electric field has units volts/meter. Thus, again referring to figure 1, we can setE=H v

D.

Equation 10 becomes:

HV

D=v dB (eqn. 11)

Finally, substituting in equation 4 and multiplying by D, we arrive at the Hall Voltage formula:

H v=D IBnT D

=( InT )∗B (eqn. 12)

Page | 7

While equation 12 looks about as clean as clean gets, therein lies a problem with the term in

parenthesis. N can, by no means available today, be measured directly or even guessed.

Typically, there are somewhere on the order of 1010 electrons that accumulate on the surface of

a semiconductor at low currents. However, while we mentioned earlier that direct

measurement of Hall Potentials require rather precise, high-quality equipment, we were able to

utilize such gear in our attempt at this lab. Naturally, magnetic field is easily measureable with

a standard gauss meter. Thus, our notation used in equation 12 has become clear, as InT

represents the slope of two measurable quantities. The most efficient way to solve for n, our

ultimate goal, is to measure the Hall Potential at different current and field strengths and

obtain the slope of the subsequent graph. From this, the charge carrier density in the

accumulation can be found using simple algebra:

n= Islope∗T (eqn. 13)

To place n into perspective, electrons wield a mass on the order of 10-31kg while the mass of

silver roughly 0.5 kg. Thus, we will expect the density of particles in the accumulation to be

very large.

Apparatus

Page | 8

While the theory behind the Hall Potential may have come across as relatively simple,

the equipment used to experimentally achieve it was not. This lab utilized a slew of meters, a

standalone, dedicated, water-cooled, DC power source, and a 3-Tesla Walker Scientific

electromagnet as seen in figure 2. Starting with the meters, we were required to monitor the

Hall Voltage, current, and field strength simultaneously. Thus, we were given a voltmeter that

read voltage to the order to 10-5 volts and auto-compensated jitters, a battery-operated

ammeter, and a gaussmeter. All were pre-assembled and pre-calibrated as we arrived to carry

out the lab procedure. A photo of the meters can be viewed in figure 3 below. The power

supply played an important role in our ability to follow through with this lab. As noted in the lab

handout9, at maximum current the electromagnet consumes 8500 Watts of power. At this level

of consumption, we were required to cool and operate a DC power supply coupled to an

entirely different breaker from the rest of the room. The cooling water stemmed from the local

watershed, and was used to cool both the DC power supply and the electromagnet. Also

pictured in figure 3 is the current generator used to move charge carriers through the silver

plate. Lastly, the device of interest (Silver plate) can be viewed in figure 2 centered between

the North and South poles of the electromagnet. The North end of the magnet is located on

Page | 9

the left, while the South resides on the right. Thus, the orthogonal magnetic field points from

left to right (North-to-South) in figure 2. Meanwhile, the conventional current flow moves from

back to front in the Hall device. Consequently, we should expect the negative charge

accumulation to reside at the top of the device. We shall return to this topic in the discussion

section when we hypothesize positive charge carrier movement and its effects.

Procedure

Due to the very sensitive, (and not to mention expensive), nature of the equipment

present for this experiment, the procedure we followed was rather rigorous and static. In other

words, the only acceptable methodology to use in performing this experiment was to follow

that stated in the lab report. In order to ensure proper startup of the electromagnet, Dr. Greg

Latta (Instructor, Professor of Physics) made a brief appearance to oversee our procedure. To

begin, we switched on the power strip that served the voltmeter, ammeter, and gauss meter

and followed this by switching on the three respective meters. Next, we switched on the DC

power supply and the water coolant that served it. Before doing this, however, it was of utmost

importance that the coarse, medium, and fine knobs were all set to zero on the power supply.

This is due to the fact that a sudden increase or decrease in power to the electromagnet could

cause severe damage to the internal components. As we activated the water coolant, the

power supply required monitoring until a light designating sufficient water flow was galvanized.

Once this occurred, we were able to switch on the current supply and set it to 5.0 Amps. At this

point the voltmeter displayed a relatively large potential even though no current was passing

through the Hall device. We will return to this in the discussion section, but for now it is

Page | 10

sufficient to say that adjusting the Hall device and auto-compensating the “jitter” on the

voltmeter was adequate to begin our data gathering. The actual data acquiring section of the

lab simply required the magnetic field to be increased in increments of 0.1 Tesla. At each

increment we entered the Hall Potential into our pre-constructed Microsoft Excel spreadsheet.

This spreadsheet enabled us to view the linear curve between Hv and B in real time. We

divvied the tasks amongst the two of us. While I was responsible for reading the Hall Potential

and entering the data into Excel, Joseph operated the DC power supply. Even after

compensation, jitter was still present in the Hall Potential. Thus, we were required to average

the value on the fly, as waiting too long to gather a reading could potentially introduce negative

effects. Also worth noting, the Voltmeter was set to a scale of 10-5V. Hence, we were forced to

quickly convert the measurement into microvolts by multiplying the raw data by ten. We

continued this trend until reaching a magnetic field of two tesla. At this point, we brought the

DC power, and the subsequent field, back down to zero. We repeated this process again for a

current of 10 Amps, and again at 15 Amps. A new auto-compensation was required between

each run. At the conclusion of the lab, we ensured that both the current and DC power was set

to zero. At this moment, all devices were turned off and the water coolant was stoppered.

Sample Calculations

Page | 11

Figure 4: The graph resulting from our first run with a current of 5 Amps (Refer to the accompanying spreadsheet for the graphs pertaining to runs 2 & 3)

Figure 4 depicts the graph we achieved from the data of our first run. Looking at our coefficient

of determination, we see that our data almost perfectly fits the linear relationship as predicted

by equation 12. I feel as though it is important, at this point, to express the expected value for

the charge carrier density in units of electrons-per-meter cubed in order to compare sample

values to it. That value is: 6.9x1028 e

m3. You may view our experimental values for charge

carrier density in the appendix of this report. The formula we utilized to achieve those values is

shown below:

ne=( B6SLOPE (B8:B27 , A 8 :A 27 )∗$ B$ 4

∗106)1.6 x10−19

(1)

We wish to check this algorithm by performing a sample calculation of our own. In this

example I will use the data points B = 1.0T and B = 1.1T from our first run using I = 5A. Thus,

9.2 μV=m∗(1.0T )+B∧10.0 μV=m∗(1.1T )+B

Page | 12

0.0 0.5 1.0 1.5 2.0 2.50.002.004.006.008.00

10.0012.0014.0016.0018.0020.00

f(x) = 8.23233082706767 x + 1.13105263157895R² = 0.999337996081445

Hall Voltage vs. Magnetic Field Strength when I = 5 A

Field Strength (T)

Hall

Volta

ge (μ

V)

Where m denotes the slope of the line formed by this data and B represents the y-axis

intercept. If we subtract the two equations, we achieve:

0.8 μV=m∗0.1T→m=0.8 μV0.1T

=8 μAm2

Looking at figure 1, we see that our slope was 8.2μA

m2, so we can be sure our methodology is

correct so far. Next, we use the data point B = 1.0T and our newfound slop to solve for B:

9.2 μV=8 μAm2

∗(1.0T )+B→B= 9.2 μV

8μA∗Tm2

= 1.15μV

Again, this closely matches our actual value for the intercept of 1.1311μV. While B was found

primarily for justification, the slope is where our interests lie. We can now apply equation

twelve to the slope and attempt to attain a value for the carrier density using two data points:

slope=8 μAm2

= InT (2)

We already know the current as it was set to roughly 5 amps. Likewise, T (plate thickness) is a

constant given in the lab handout to be 5.41x10-5m. Thus, we rearrange (2) using equation 13

to solve for n as follows:

n= Islope∗T

= 5 A

8μA

m2∗5.41∗10−5m

=1.55 x104 μCm3 (3)

In this state, the charge carrier density doesn’t really tell us much. Our goal is to find the

amount of electrons per meter cubed. First, we multiply (3) by 106 to achieve a value in

Page | 13

coulombs:

n=1.55x 104μC

m3∗( 1C

10−6μC )=1.55x 1010 Cm3 (4)

Lastly, we apply the fact that one electron exhibits a charge of 1.60x10-19C. Thus, we divide (4)

by this value to achieve our sought after value in units of e

m3:

ne=1.55 x 1010 C

m3∗( e

1.60 x10−19C )=7.22 x1028 em3

Considering the massive number of electrons accumulating on this piece of silver, it seems

rather amazing that we come so close to the expected value with only two data points. We can

perform a sample error calculation relative to the expected value shown below:

% error=¿n0−ne∨¿n0

∗100%=|6.9−7.22|

6.9∗100%=4.64%¿

This is an almost insignificant error considering the sizes of the values. Thus, as we have

demonstrated over the previous two pages, we can be very sure that our excel spreadsheet

algorithms, graphs, and final values are correct and within reason.

Discussion

Upon averaging the values for ne acquired after three runs, we achieved a final value of:

Page | 14

ne=7.07 x 1028 e

m3

As stated in the previous section, the accepted value of ne, according to the lab handout, was

6.9x1028 e

m3. Consequently, we calculate our relative error as we did before (The factors of 1028

all cancel out):

%Relative Error=|6.9−7.07|

6.9∗100% = 2.46% error

This is a rather exceptional error, and, after reviewing our stellar coefficients of determination

and our lack of any setbacks whatsoever during the course of our lab, truly wraps up a

successful experiment. This error comes off as insignificant due to the fact that the size of our

“sample” is on an order to which nothing else on earth compares to (other than more atoms).

Even the farthest galaxy currently known, Abell 1835 IR191, is only 13 billion light years

(1.3x1010) away.10 Our density is more than a billion billion times larger that that distance.

Thus, the fact that in half an hour we were able to achieve a roughly 2% error on this quantity

simply with a volt and gauss-meter is simply extraordinary.

As we mentioned in the procedure section, we were forced to auto-compensate for

large potentials that would accumulate before any current was activated. This phenomenon is

known as thermo-couple potential creation, and it is due to the temperature gradient between

the junctions located throughout the device. When there is temperature difference between

two conductors two important phenomena occur: Heat flow, and what is coined as the

Seebeck effect.11 We are only concerned with the latter. The Seebeck effect concerns the fact

Page | 15

Figure 5: The Hall Effect Device

that energetic electrons will move from the hot junction to the cooler one while pushing some

of the lesser energy electrons with them. In turn, this causes a potential difference between

the hot and cold ends, and, alas, a thermocouple potential is born. Considering the fact that

not only did we perform this lab early in the morning, but we were the first to perform it that

day, we likely had to compensate for more of this potential than one normally would. Likewise,

this may have been a source of some of the error we did garner as the junctions and conductors

heated up over the course of the experiment. You might notice that our first run returned a

value a bit lower than the other two. I postulate that this is due to the heating of the wires over

the first run, in turn, throwing off our initial compensation.

Next we consider the situation in which

positive charge carriers would have moved

through the Hall Device. Technically, this

effect transpires from the movement of

“holes” in the metal; not protons. However,

for simplicity, we will use the term

“protons” in place of positive charge

carriers. If we assume the protons to be

moving from the back of the Hall Device

(see figure 5) to the front, then, using the

same directional convention as before, the

velocity of the protons has a directional vector

in the positive x, or i, direction. The magnetic

Page | 16

field does not change. Thus, it continues to move from North to South in the negative z, or -k ,

direction. We will again make use of equation 6 to qualitatively observe the physics of positive

charge movement. Summing up:

v protons=i∧B=− k∧q=+e

Therefore:

FB=¿

By this prediction, if protons truly are the charge carriers moving through the Hall Device, the

polarity of the charge accumulation is reversed, as positive charge now occupies the top of the

silver slab. While, theoretically, the absolute value to the Hall Potential should remain the

same, the field is reversed as protons move through the metal.

Further proof that thermocouple potentials likely played a role in our first run is the peculiar

jump in our value for ne between the first run and the other two. Runs two and three returned

almost the exact same value, while the first run, although closer to the expected value n0, was

the odd ball. At first glance, we figured that this was likely due to an increased current, which

subsequently allowed for a greater amount of electrons to be pushed to the top. However,

looking more carefully at equations 12 and 13, while the slope varies linearly with current, the

value of ne has an inverse relationship with this increased current. Thus, in theory, the increase

in current should be cancelled out by the increase in slope, and ne should remain constant.

Therefore, returning to our original prediction, we feel as though the variance in our first run

was due to a cold apparatus exhibiting thermocouple potentials.

Page | 17

One interesting phenomena we were unable to experiment with in our lab session is the

moving of the conductor itself. Naturally, equation 6 is only concerned with the movement of

the electrons relative to the electro magnet (or, specifically, the electric field). Thus, we can

hypothesize that if we were to move the entire Hall Device in the opposite direction of the

current (in our case, toward the back of the electromagnet) at the exact speed as the electron

drift speed, then the motion of the electrons would be zero relative to the field. If this is the

case, then equation 6 zeros out and we have a magnetic force of exactly zero. Succinctly, if we

move the Hall device at an equal and opposite velocity relative to the electrons inside, we will

not observe a Hall potential! Achieving this even near-perfectly in the lab setting would be

rather difficult. However, the theory further solidifies the relation between magnetic fields and

charge carriers.

Although 19th century scientific advancement hinders us from directly comparing our value of

electron density with Hall’s, we can qualitatively appreciate the rigor involved in his finding of

such a remarkably small potential difference. Nonetheless, the effect has found applications far

and wide due to its ability to give a clean on-off signal. While the classical Hall Effect, at this

point, may be fully understood, its extensions into the quantum world will likely be a topic of

heated debate and research for years to come.

Page | 18

Works CitedCain, F. (2004, March 1). Record for Furthest Galaxy is Broken Again. Retrieved October 30,

2010, from Universe Today: http://www.universetoday.com/9347/record-for-furthest-galaxy-is-broken-again/

Georgia State University. (n.d.). The Hall Effect. Retrieved October 30, 2010, from HyperPhysics: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

Honeywell. (n.d.). Hall Effect Sensing and Application. Retrieved October 30, 2010, from Honeywell: http://content.honeywell.com/sensing/prodinfo/solidstate/technical/hallbook.pdf

Hugh D. Young, R. A. (2007). University Physics. Pearson Addison-Wesley.

Latta, D. G. (n.d.). The Hall Effect in Silver Notes. Frostburg: Frostburg State University.

Microstar Laboratories. (2009). Thermocouple Cold Junctions. Retrieved October 30, 2010, from Microstar Laboratories: http://www.mstarlabs.com/sensors/thermocouple-cold-junctions.html

Qiu, Y. (1997, April 27). Basics of Hall Effect: History. Retrieved October 30, 2010, from Johns Hopkins University: http://www.pha.jhu.edu/~qiuym/qhe/node1.html

Page | 19

ENDNOTES

Page | 20

APPENDIX - RAW DATA

Current: 4.98 A Current: 10.01 A Current: 15.01 A

B (T) Hv (μV) Reading B (T) Hv (μV) Reading B (T) Hv (μV) Reading

0.1 2.00 0.20 0.1 1.60 0.16 0.1 2.50 0.25

0.2 2.90 0.29 0.2 3.00 0.30 0.2 5.30 0.53

0.3 3.70 0.37 0.3 4.60 0.46 0.3 7.40 0.74

0.4 4.50 0.45 0.4 6.20 0.62 0.4 9.60 0.96

0.5 5.30 0.53 0.5 7.80 0.78 0.5 12.50 1.25

0.6 6.00 0.60 0.6 9.60 0.96 0.6 14.90 1.49

0.7 7.00 0.70 0.7 11.10 1.11 0.7 17.50 1.75

0.8 7.70 0.77 0.8 12.90 1.29 0.8 19.80 1.98

0.9 8.30 0.83 0.9 14.10 1.41 0.9 22.30 2.23

1.0 9.20 0.92 1.0 16.10 1.61 1.0 24.50 2.45

1.1 10.00 1.00 1.1 17.60 1.76 1.1 27.10 2.71

1.2 10.80 1.08 1.2 19.20 1.92 1.2 29.60 2.96

Page | 21

1.3 11.70 1.17 1.3 21.00 2.10 1.3 32.00 3.20

1.4 12.70 1.27 1.4 22.50 2.25 1.4 34.20 3.42

1.5 13.50 1.35 1.5 24.40 2.44 1.5 36.80 3.68

1.6 14.40 1.44 1.6 25.90 2.59 1.6 39.40 3.94

1.7 15.30 1.53 1.7 27.40 2.74 1.7 41.90 4.19

1.8 16.10 1.61 1.8 29.20 2.92 1.8 44.10 4.41

1.9 16.80 1.68 1.9 30.50 3.05 1.9 46.50 4.65

2.0 17.60 1.76 2.0 32.10 3.21 2.0 48.60 4.86

n = 1.1182E+10 C/m^3 n = 11387638878 C/m^3 n = 1.14E+10 C/m^3

ne = 6.9886E+28 e/m^3 ne = 7.11727E+28 e/m^3 ne = 7.11E+28 e/m^3

ne-avg = 7.07315E+28 e/m^3

Page | 22

APPENDIX - DISC CONTENTS

ROOT DIRECTORY

O LAB 4 – HALL EFFECT.DOC

THE OFFICIAL MICROSOFT WORD LAB REPORT CONCERNING THE HALL EFFECT IN SILVER

O HALL EFFECT SPREADSHEET.XLS

THE MICROSOFT EXCEL SPREADSHEET CONTAINING THE RAW DATA ENTERED DURING THE COURSE OF THE LAB

O HALLV7.PNG

FIGURE 1 USED IN THIS LAB REPORT

O FIGURE2.PNG

FIGURE 2 USED IN THIS LAB REPORT

O IMG_1279.JPG

FIGURE 3 USED IN THIS LAB REPORT

O IMG_1277.JPG

FIGURE 5 USED IN THIS LAB REPORT

Page | 23

1 Edwin Hall (1879). "On a New Action of the Magnet on Electric Currents". American Journal of

Mathematics (American Journal of Mathematics, Vol. 2, No. 3) 2 (3): 287–92. doi:10.2307/2369245. Retrieved

2010-10-30

2 Georgia State University. (n.d.). The Hall Effect. Retrieved October 30, 2010, from HyperPhysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

3 Qiu, Y. (1997, April 27). Basics of Hall Effect: History. Retrieved October 30, 2010, from Johns Hopkins University:

http://www.pha.jhu.edu/~qiuym/qhe/node1.html

4 See3: Applications

5 Klitzing, K. von; Dorda, G.; Pepper, M. (1980). "New Method for High-Accuracy Determination of the Fine-Structure

Constant Based on Quantized Hall Resistance". Phys. Rev. Lett. 45 (6): 494–49

6 "Press Release: The 1985 Nobel Prize in Physics". Nobelprize.org. 30 Oct 2010

http://nobelprize.org/nobel_prizes/physics/laureates/1985/press.html

7 Honeywell. (n.d.). Hall Effect Sensing and Application. Retrieved October 30, 2010, from Honeywell:

http://content.honeywell.com/sensing/prodinfo/solidstate/technical/hallbook.pdf

8 Hugh D. Young, R. A. (2007). University Physics. Pearson Addison-Wesley.

9 Latta, D. G. (n.d.). The Hall Effect in Silver Notes. Frostburg: Frostburg State University.

10 Cain, F. (2004, March 1). Record for Furthest Galaxy is Broken Again. Retrieved October 30, 2010, from Universe Today: http://www.universetoday.com/9347/record-for-furthest-galaxy-is-broken-again/

11 Microstar Laboratories. (2009). Thermocouple Cold Junctions. Retrieved October 30, 2010, from Microstar Laboratories: http://www.mstarlabs.com/sensors/thermocouple-cold-junctions.html