hall effect experiment engineering physics

• Electromagnetism

Hall Effect

Hall effect is a process in which a transverse electric field is developed in a solid material when the material carrying an electric current is placed in a magnetic field that is perpendicular to the current. The Hall effect was discovered by Edwin Herbert Hall in 1879. In this article, let us learn about the Hall effect in detail.

Principle of Hall effect

The principle of the Hall effect states that when a current-carrying conductor or a semiconductor is introduced to a perpendicular magnetic field, a voltage can be measured at the right angle to the current path. This effect of obtaining a measurable voltage is known as the Hall effect.

When a conductive plate is connected to a circuit with a battery, then a current starts flowing. The charge carriers will follow a linear path from one end of the plate to the other end. The motion of charge carriers results in the production of magnetic fields. When a magnet is placed near the plate, the magnetic field of the charge carriers is distorted. This upsets the straight flow of the charge carriers. The force which upsets the direction of flow of charge carriers is known as Lorentz force .

Due to the distortion in the magnetic field of the charge carriers, the negatively charged electrons will be deflected to one side of the plate and positively charged holes to the other side. A potential difference, known as the Hall voltage will be generated between both sides of the plate which can be measured using a metre.

The Hall voltage represented as V H is given by the formula:

I is the current flowing through the sensor

B is the magnetic field strength

q is the charge

n is the number of charge carriers per unit volume

d is the thickness of the sensor.

Similar Reading:

Hall Coefficient

The Hall coefficient R H is mathematically expressed as

Where j is the current density of the carrier electron, Ey is the induced electric field and B is the magnetic strength. The hall coefficient is positive if the number of positive charges is more than the negative charges. Similarly, it is negative when electrons are more than holes.

Applications of Hall Effect

Hall effect principle is employed in the following cases:

• Magnetic field sensing equipment
• For the measurement of direct current, Hall effect Tong Tester is used.
• It is used in phase angle measurement
• Proximity detectors
• Hall effect Sensors and Probes
• Linear or Angular displacement transducers
• For detecting wheel speed and accordingly assist the anti-lock braking system.

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Frequently Asked Questions – FAQs

Name one practical use of hall effect..

Hall effect is used to determine if a substance is a semiconductor or an insulator. The nature of the charge carriers can be measured.

How is Hall potential developed?

When a current-carrying conductor is in the presence of a transverse magnetic field, the magnetic field exerts a deflecting force in the direction perpendicular to both magnetic field and drift velocity. This causes charges to shift from one surface to another thus creating a potential difference.

What is a Hall effect sensor?

A Hall effect sensor is a device that is used to measure the magnitude of a magnetic field.

In the Hall effect, the direction of the magnetic field and electric field are parallel to each other. True or False?

False. The magnetic field and electric field are perpendicular to each other.

Explain Lorentz Force.

Lorentz force is the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Hall Effect in Physics

The Hall effect is a phenomenon in physics that occurs when a magnetic field is applied perpendicular to the flow of current in a conductor or semiconductor. This results in the development of a transverse voltage, known as the Hall voltage, across the material. Understanding the Hall effect is crucial because it provides insights into the behavior of charge carriers in materials. The effect has significant implications in various fields, from fundamental physics to practical applications in electronic devices.

What Is the Hall Effect?

The Hall effect describes the generation of a voltage difference (Hall voltage) across an electrical conductor through which an electric current is flowing, when a magnetic field is applied perpendicular to the current. This effect was discovered by Edwin Hall in 1879 and is a critical tool in the study of electronic properties of materials.

Importance of the Hall Effect

The Hall effect is important because it allows for the determination of the type (positive or negative), density, and mobility of charge carriers in a material. It is particularly useful in the characterization of semiconductors and in the design of various electronic components and sensors.

American physicist Edwin Herbert Hall discovered the Hall effect in 1879 while working on his doctoral thesis at Johns Hopkins University. He observed that placing a current-carrying conductor in a perpendicular magnetic field generates a voltage across the conductor in a direction perpendicular to both the current and the magnetic field. This discovery provided a new way to probe the properties of conductors and semiconductors, significantly advancing the field of solid-state physics. Keep in mind, Hall’s observation occurred prior to the discovery of the electron.

Theory Behind the Hall Effect

The Lorentz force explains the Hall effect. The Lorentz force acts on the moving charge carriers in the presence of a magnetic field. When a current flows through a conductor in the presence of a perpendicular magnetic field, the charge carriers (electrons or holes) experience a force that is perpendicular to both the current direction and the magnetic field. Positive and negative charges move in opposite directions. Charge carriers accumulate on one side of the conductor, creating a voltage difference across the conductor, known as the Hall voltage.

Positive Charge Carriers

In situations involving metal wires, the charge carriers are electrons. In semiconductors, charge carriers can be holes (with electrons moving in the opposite direction). However, sometimes current involves positive charge carriers. Examples include:

• Ionic Conductors : In ionic conductors, the charge carriers are electrolytes , which are ions.
• Plasma : There are both electrons and free positive ions in plasma. Examples of environments involving plasma include stars, neon signs, and plasma televisions.
• Solid-State Materials : The primary charge carriers are ions with positive charges in certain ionic crystals or superconductors.

Hall Voltage Formula

Calculate the Hall voltage (VH) using the following formula:

V H = B · I / n · q · d

• B is the magnetic field strength (in Tesla, T),
• I is the current through the conductor (in Amperes, A),
• n is the charge carrier density (in carriers per cubic meter, m -3 ),
• q is the charge of the carriers (in Coulombs, C),
• d is the thickness of the conductor (in meters, m).

Example Problem

For example:

A copper strip of thickness 0.01cm is in a magnetic field of 0.5T. A current of 3 A flows through the strip. Given that the charge carrier density in copper is approximately 8.5×10 28  m −3 and the charge of an electron is 1.6×10 −19  C, calculate the Hall voltage.

• Convert Thickness to Meters: 𝑑 = 0.01 cm = 0.01×10 −2  m = 1×10 −4  m
• Identify Given Values: 𝐵 = 0.5 T 𝐼 = 3 A 𝑛 = 8.5×1028 m −3 𝑞 = 1.6×10 −19  C
• Plug the Values into the Hall Voltage Formula: 𝑉 𝐻 = 𝐵⋅𝐼 / 𝑛⋅𝑞⋅𝑑 = 0.5 T ⋅ 3 A / 8.5×10 28  m −3 ⋅ 1.6×10 −19  C ⋅ 1×10 −4  m
• Calculate the Denominator: 𝑛⋅𝑞⋅𝑑 = 8.5×10 28 ⋅ 1.6×10 −19 ⋅ 1×10 −4 𝑛⋅𝑞⋅𝑑 = 8.5×1.6×10 28−19−4 𝑛⋅𝑞⋅𝑑=13.6 × 10 5
• Calculate the Hall Voltage: 𝑉 𝐻 = 0.5 ⋅ 3 / 13.6×10 5 𝑉 𝐻 = 1.5 / 13.6×10 5 𝑉 𝐻 = 1.10×10 −6  V V H ​= 1.10 μ V

Result: The Hall voltage across the copper strip is 1.10 𝜇V.

The Hall Coefficient

The Hall coefficient (R H ) is a fundamental parameter that characterizes the Hall effect in a material. It is the ratio of the induced electric field (Hall voltage) to the product of the current density and the applied magnetic field. Mathematically, the Hall coefficient is:

R H = E H / J · B​​

• E H ​ is the Hall electric field,
• J is the current density,
• B is the magnetic field.

The Hall coefficient provides information about the type and density of charge carriers in the material. For a material with positive charge carriers (holes or cations ), the Hall coefficient is positive, and for negative charge carriers (electrons or anions), it is negative.

Using the Right-Hand Rule with the Hall Effect

The right-hand rule is a simple mnemonic for determining the direction of the Hall voltage. According to this rule, if you point the thumb of your right hand in the direction of the current and your index finger in the direction of the magnetic field, your middle finger (perpendicular to both the thumb and index finger) points in the direction of the induced Hall voltage.

What Is a Hall Effect Sensor?

A Hall effect sensor is a transducer that varies its output voltage in response to changes in the magnetic field. These sensors are used to detect the presence, absence, or strength of a magnetic field. They are commonly used in applications such as:

• Automotive Ignition Systems : For determining the position of the crankshaft or camshaft.
• Proximity Sensors : For detecting the proximity of objects in automated systems.
• Speed Detection : In tachometers and anti-lock braking systems (ABS).
• Current Sensing : In power supplies and battery management systems.
• Nondestructive Testing : Sensors detect defects and irregularities, with applications in crack detection and thickness measurements.

Hall Effect Controllers and Joysticks

Hall effect controllers and joysticks utilize Hall sensors for detecting the position of a control stick or lever. Unlike traditional potentiometers, Hall effect sensors do not suffer from mechanical wear and tear. Thus, they offer more reliable and longer-lasting performance. These controllers find use in various applications, including gaming, aviation, and industrial control systems.

Applications of the Hall Effect

The Hall effect has numerous applications, including:

• Hall Effect Sensors : These devices use the Hall effect to measure magnetic field strength. They are popular in automotive, industrial, and consumer electronics for applications like current sensing, position sensing, and speed detection. The sensors also find use in blood flow meters and magnetically activated implants (e.g., cochlear implants) in medicine and biology.
• Magnetic Field Measurement : The Hall effect determines the strength and direction of magnetic fields in various scientific and industrial applications.
• Semiconductor Characterization : The Hall effect determines the carrier concentration, mobility, and type in semiconductors, which is essential for designing and optimizing electronic devices.
• Space Exploration : Hall effect thrusters are ion thrusters for spacecraft propulsion. The Hall effect also measures properties of plasma in space environments.

Additionally, the effect is important in fusion research and in understand star formation.

Quantum Hall Effect

The quantum Hall effect occurs in two-dimensional electron systems subjected to low temperatures and strong magnetic fields. A characteristic of the quantum Hall effect is the quantization of the Hall conductance in integer multiples of a fundamental constant. This discovery was made by Klaus von Klitzing in 1980.

Spin Hall Effect

The spin Hall effect is a phenomenon where an electric current flowing through a material with strong spin-orbit coupling generates a transverse spin current, leading to spin accumulation on the material’s edges. This effect is essential for spintronics, a field of study that develops electronic devices based on electron spin rather than charge.

Experimental Setup for Measuring the Hall Effect

Measuring the Hall effect involves a set-up for observing the transverse voltage generated across a material when an electric current flows through it in the presence of a perpendicular magnetic field. Here’s a detailed description of the experimental setup and procedure:

Experimental Setup

• Hall Bar Sample : A rectangular strip of the material (conductor or semiconductor). The dimensions of the sample should be well-defined, especially the thickness (𝑑).
• Constant Current Source : A DC power supply that provides a stable and known current (𝐼) through the Hall bar sample.
• Magnetic Field Source : Typically an electromagnet or a permanent magnet capable of generating a uniform magnetic field (𝐵) perpendicular to the current flow in the sample. Make sure the strength of the magnetic field is adjustable and measurable.
• Voltmeter : Use a sensitive voltmeter or a digital multimeter for measuring the Hall voltage (𝑉 𝐻 ) across the sample. Connect the voltmeter to the sides of the Hall bar where the voltage develops.
• Positioning Apparatus : Use clamps or other equipment that secures the Hall bar sample in place and ensures that the magnetic field is perpendicular to the current flow.
• Temperature Control (Optional) : If the experiment requires measurements at different temperatures, include a temperature-controlled environment or a heating/cooling apparatus.
• Cut the sample into a rectangular strip with well-defined dimensions.
• Attach electrical contacts to the ends of the sample for the current and to the sides for measuring the Hall voltage.
• Connect the sample to the constant current source, ensuring that the current flows uniformly through the length of the Hall bar.
• Connect the voltmeter across the sides of the sample.
• Place the sample in the magnetic field generated by the electromagnet or permanent magnet.
• Ensure that the magnetic field is perpendicular to the plane of the Hall bar sample and the direction of the current.
• Adjust and measure the strength of the magnetic field using a gaussmeter or a similar device.
• Turn on the current source and set the desired current (𝐼) through the Hall bar.
• With the magnetic field applied, read the Hall voltage (𝑉 𝐻 ) from the voltmeter. This voltage is the potential difference across the width of the sample due to the Hall effect.
• Repeat the measurements for different values of the magnetic field strength (𝐵) and current (𝐼) to study the dependence of the Hall voltage on these parameters.
• Optionally, repeat the measurements at different temperatures if temperature control is available.

Data Analysis

• Using the measured Hall voltage (𝑉 𝐻 ​), current (𝐼), magnetic field strength (𝐵), and thickness of the sample (𝑑), calculate the Hall coefficient (𝑅 𝐻​ ) using the formula: 𝑅𝐻 = 𝑉 𝐻 ⋅𝑑 / 𝐼⋅𝐵​
• The sign of the Hall coefficient indicates the type of charge carriers: positive (𝑅 𝐻 > 0) for holes and negative (𝑅 𝐻 < 0) for electrons.
• Use the magnitude of 𝑅 𝐻 for calculating the charge carrier density (𝑛) using the relationship: 𝑛 = 1 / 𝑅 𝐻 ⋅𝑞​ where 𝑞 is the charge of the carrier (e.g., 1.6×10 −19  C for electrons).
• Calculate the mobility (𝜇) of the charge carriers if the conductivity (𝜎) of the material is known: 𝜇 = 𝜎 / 𝑛⋅𝑞​
• Braiding, C. R.; Wardle, M. (2012). “The Hall effect in star formation”. Monthly Notices of the Royal Astronomical Society . 422 (1): 261. doi: 10.1111/j.1365-2966.2012.20601.x
• Hall, Edwin (1879). “On a New Action of the Magnet on Electric Currents”. American Journal of Mathematics . 2 (3): 287–92. doi: 10.2307/2369245
• Karplus, R.; Luttinger, J. M. (1954). “Hall Effect in Ferromagnetics”. Phys. Rev . 95 (5): 1154–1160. doi: 10.1103/PhysRev.95.1154
• Ohgaki, Takeshi; Ohashi, Naoki; et al. (2008). “Positive Hall coefficients obtained from contact misplacement on evident n-type ZnO films and crystals”. Journal of Materials Research . 23 (9): 2293. doi: 10.1557/JMR.2008.0300
• Ramsden, Edward (2011). Hall-Effect Sensors: Theory and Application . Elsevier. ISBN 978-0-08-052374-3.

Related Posts

• Hall Effect
• 1.1.1 Part 1: Normal circuit (No Magnetic Field Yet)
• 1.1.2 Part 2: Initial Transient State (Magnetic Field Present)
• 1.1.3 Part 3: Steady State (Magnetic Field Still Present, but abated)
• 1.2.1 Part 1: Normal circuit (No Magnetic Field Yet)
• 1.2.2 Part 2: Initial Transient State (Magnetic Field Present)
• 1.2.3 Part 3: Steady State (Magnetic Field Still Present, but abated)
• 1.3.1 Part 1: Normal circuit (No Magnetic Field Yet)
• 1.3.2 Part 2: Initial Transient State (Magnetic Field Present)
• 1.3.3 Part 3: Steady State (Magnetic Field Still Present, but abated)
• 1.4.1 Simple
• 1.4.2 Middling
• 1.4.3 Difficult
• 1.5.1 Industrial
• 1.5.2 Laboratory
• 1.6 History
• 1.7 Conclusion: Tips to remember
• 1.8.1 Further reading
• 1.8.2 External links
• 1.9 References

Edited by Adeline Boswell Fall 2019, Edited by Alayna Baker Spring 2020

The Hall Effect is the electric polarization of a block or slab of metal that occurs when a current is run through it while it is subject to a magnetic field perpendicular to the current.

The Main Idea

When a mobile charge, either positive or negative, flows through a metal block and is influenced by a magnetic field, the magnetic force on the charges force them to begin concentrating on one side of the block. Thus the block polarizes and has negative charges on one side and positive on the other in order to remain neutral. This grouping of positive charges in one part of the block and negative charges in another part of the block creates an electric field and thus an electric force equal on magnitude to the magnetic force that causes the initial polarization, but opposite in direction. The magnetic and electric forces cancel each other out and after some time, the charges flow normally through the block and do not group on one side or the other of the block. This perpendicular electric field also creates a potential difference known as the "Hall Voltage."

Part 1: Normal circuit (No Magnetic Field Yet)

(For simplicity, the mobile charges in this example have already been determined to be negatively charged electrons. This will not always be the case and it should not be assumed that the mobile charges are electrons)

Mobile electrons flow through a wire due to a parallel electric field inside the wire. This electric field is caused by an energy source, most commonly a battery. The parallel electric field flows from an area of high potential (i.e. the positive end of the battery) to an area of low potential (i.e. the negative end of the battery). This is the same direction as the conventional current. Since electrons are negatively charged, they flow in the opposite direction of the parallel electric field.

Part 2: Initial Transient State (Magnetic Field Present)

Mobile electrons are subjected to a magnetic field perpendicular to their motion as they flow through the wire. This results in the mobile charges being forced onto one side of the block by the magnetic force. This grouping of mobile charges on one side of the block creates an electric force. As time passes, more mobile charges are deposited on the side of the block and the electric force increases in magnitude.

Part 3: Steady State (Magnetic Field Still Present, but abated)

Over time massive quantities of charges are concentrated on one side of the block. As the charges build up, they will begin to create a charged area on one surface of the conductor. The charged surface will create an electric force to oppose the magnetic force that is pushing new electrons onto this charged surface. This opposing electric force is called the transverse electric force. When enough mobile charges have collected, their combined transverse electric force will be equal in magnitude to the magnetic force that is holding them. At this point, there is no net vertical force pushing more electrons against the surface of the conductor and these electrons will flow normally again, as they would if there was no magnetic field present. This is called the steady state.

A Mathematical Model

[math]\displaystyle{ F_{electric, parallel} = qE_{parallel} }[/math]

Where q is the electric charge of the mobile charge. As F and E are vectors, a negative charge results in an electric force in the opposite direction of the electric field.

[math]\displaystyle{ F_{magnetic} = q(v\; &Chi; \;B) }[/math]

Where v is the velocity of the mobile charge and B is the magnetic field. For help calculating the cross product, including an example using the Hall Effect, see Right-Hand_Rule . REMEMBER, the mobile charge will move in the opposite direction of the cross product if it is negative, similar to how it behaves in an electric field.

[math]\displaystyle{ F_{electric, perpendicular} = qE_{perpendicular} }[/math]

[math]\displaystyle{ |F_{electric, perpendicular}| = |F_{magnetic}| }[/math]

Computational Model

In this diagram, it is assumed the charge carrier is a negatively charged electron. THIS IS NOT A SAFE ASSUMPTION on a real question, experiment, or exam but was done for the purpose of simplifying explanations.

In this diagram a solid conductive metal block is connected to two ends of a battery by wires. At this time there is no magnetic field present and electrons flow through the block in a straight line from wire to wire without interference or interruption.

In this diagram the circles containing x's represent a magnetic field (NOT a magnetic force) into the page. When the electrons begin to move across the block their initial velocity interacts with the magnetic field to create a magnetic force downward. This causes electrons to begin pooling on the bottom face of the slab. This polarizes the block and creates a vertical potential difference across the block. It also creates an electric force that opposes the magnetic force, but in this state it is smaller than the magnetic force, resulting in continued pooling of electrons.

As time passes eventually sufficient quantities of electrons build up to create an electric force equal in magnitude to the magnetic force but opposite in direction. This allows the electrons to continue flow across the block as they did in part 1, however now the vertical voltage difference which was created in part 2 is not only still present but also at its maximum value. Most practice and exam problems will involve either the calculation or orientation of this voltage difference. It's important to remember that a voltmeter will have a positive reading if the positive node is connected to the end of the block which is positively charged and vice versa.

A metal block is connected to a battery by two wires. Conventional current flows clockwise and the mobile charge in the block is positive. The block also experiences a magnetic field out of the page denoted by concentric circles. The block is also connected to a voltmeter. The positive end of the voltmeter is connected to the bottom of the block and the negative end of the voltmeter is connected to the top of the block. See attached photo for a diagram. What sign will the voltmeter display?

Click for Solution

In this case, since magnetic force is q(v X B) and we know the charges are positive and thus follow the conventional current which moves across the block from left to right, the magnetic force points up. This means that the mobile charges (positive) will be pushed towards the bottom of the block. Remember: a voltmeter will have a positive reading if the positive end is connected to the positively charged side of the block. In this case, the bottom of the block is positively charged and the positive end of the voltmeter is connected there. The voltmeter will have a positive reading.

A battery and metal block are connected by 2 wires. Conventional current flows clockwise. A magnetic field points out of the page, denoted by concentric circles. A voltmeter is attached to the block with its positive lead at the top of the block and its negative lead at the bottom of the block. The voltmeter has a positive reading. What sign does the mobile charge have?

From the voltmeter reading we can deduce that the top of the block is positively charged and the bottom negatively charged. Thus, we check if positive mobile charge carriers satisfy this requirement. A positive charge moves with the conventional current, which in this case is from left to right, meaning its velocity would be in the positive x direction. When taking the cross product of the charge's velocity and the magnetic field (out of the page) we get a magnetic force pointing downward, thus meaning the positive charges would be forced downward as well. This is in conflict with the positive voltmeter reading and thus cannot be true. Next we check if negative charge carriers agree with the voltmeter readings. A negatively charged mobile charge carrier moves counter to the conventional current, in this case meaning it moves across the block from right to left resulting in a velocity in the negative x direction. When we take the cross product of this velocity and the magnetic field out of the page multiplied by the charge of the carrier we get a magnetic force pointing downwards (using F = q(v X B). This would result in the block's bottom being negatively charged and the top being positively charged. This result agrees with the given voltmeter reading. The mobile charge carriers are negative.

[math]\displaystyle{ B = 1.8 T }[/math] out of the page (denoted by concentric circles)

[math]\displaystyle{ n = 7*10^{25} /m^3 }[/math]

[math]\displaystyle{ u = 3*10^{-5} }[/math]

• What does reading does the voltmeter display (both magnitude and sign)?
• What does reading does the Ammeter display(both magnitude and sign?

Click for Solution to #1

Explanation: The voltmeter reads the voltage of the bar between the given distance. Since this voltmeter is attached along the height of the bar, the distance is going to be the 3cm. We write out the Lorentz Force formula and set it equal to zero, which makes the magnetic force and electric force equal to each other. After manipulating the equation, the Hall Electric Field is drift sped times the magnetic field. The drift speed is found by manipulating the Current formula, Area density formula, and the Resistance Formula. After I is found, you plug it into the I in the drift speed formula, and plug drift speed v into the Hall electric field formula. Since Hall voltage is Hall electric times the distance, you multiply the calculated Hall electric field with 3 cm in order to get the final Hall voltage.

Click for Solution to #2

[math]\displaystyle{ I = \frac{Emf*q*n*u*A}{L} }[/math]

[math]\displaystyle{ I = 2.19927 A }[/math]

Explanation: You use the derivation of I from first portion of the question and plug in the values to calculate the conventional current. The Area here is the width times the height because the Ammeter is connected through the face created by the area of width and height.

[math]\displaystyle{ B = 1.5 }[/math] T out of the page (denoted by concentric circles)

• Calculate the drift speed v of the mobile charges
• Calculate the charge density n of the mobile charges
• ∆V = 13 V along the length of the bar, calculate the mobility u of the mobile charge carrier in the metal

Explanation: First, set the Lorentz Force Equation equal to zero. After a couple of algebraic manipulations similar to the middling question, the Hall electric field equals to the product of the drift speed and magnetic field. Since, the hall electric field is not given but hall voltage is, you have to substitute the hall electric field with hall voltage divided by the height of the bar (distance that voltmeter calculated). Afterwards, plug in all the given values, and calculate for the drift speed.

Explanation: In order to find the charge density of the mobile charge carriers use the conventional current formula. Manipulate the conventional current formula to find a formula for charge density and plug in all the values.

Click for Solution to #3

Explanation: The drift speed of the charge carriers is the product of the electric field and mobility of the charge carriers. Since electric field is not given, but the voltage along the length of the bar is, you have to substitute the electric field with the given voltage divided by the length of the bar. Afterwards, plug in all the values given in the problem and the value calculated for the drift speed.

Applications

Hall effect is all about seeing the relationship between magnetic and electric forces while also remembering how metals polarize. This means that it has a lot of mechanical and machine applications. It can sense when a magnetic field or electric field changes, so it can control many machines, apply pressures, and report many values. All of these skills are very important for Mechanical Engineering, so this topic has a lot of relevance to my major. Moreover, a lot of engineering, in general, is about analyzing concepts before calculating values. The idea of the Hall Effect gives a lot of important data without the use of any numbers (of course it gives more info on the calculation of numbers). This reasoning process required for the Hall Effect is a very helpful skill for engineers to have.

Another field that takes advantage of the Hall Effect is Electrical Engineering thanks to the Hall Effect Sensor. Electrical engineers can use the hall effect sensor to record movement. As seen in the picture to the left, the sensor will increase its voltage the closer the magnet is to the sensor. In fact, a VIP group here at Georgia Tech, the VIP Hands-on Learning team, researched the possibility of using the sensor to measure the movement of a two-degree of freedom spring-mass system. Links to the VIP Research: https://vip.gatech.edu/wiki/index.php/Vibrations https://vip.gatech.edu/wiki/index.php/Hall_Effect_Sensor

Hall Effects are used in industry to aid in the control of Hydraulic systems such as moving cranes and backhoes. It is also used to help sense a car wheel's motion to aid in the use of anti-skid/anti-lock brakes. Every smartphone today uses a hall effect sensor as well. This is how the digital compass of a cell phone works. The hall effect senses the change in magnetic field to approximate direction. Another great way of using the hall effect in smartphones is to lock the screen when a case cover is flipped. The cover has a magnet that the smartphone senses, so it locks the screen automatically when the cover is on the screen. A test for this feature can be seen in the following video: https://www.youtube.com/watch?v=ITbT5vrvhX8 .

Hall effect is also taken into consideration when hall probes are used as magnetometers.

A Hall probe is used to measure the difference of magnetic flux perpendicular to its sensor. This information is then fed to magnetometers to help read the difference in magnetic fields.

Hall effect sensor: http://www.ebay.com/sch/i.html?_nkw=hall+effect+sensor

Magnetometer: http://www.ebay.com/itm/EM2-EARTH-MAGNETOMETER-MAP-MAGNETIC-FIELDS-SURVEY-TOOL-/251324557405?hash=item3a841c685d:m:m8gnViuidubx7vMbMejiNNA

To use this idea in a lab, simply create a circuit through a conductive material, like a piece of foil, and calculate the direction of the magnetic field using right-hand rule. Use this information to then properly add the hall probes to the foil so they are perpendicular to the magnetic field, and then BOOM! You will have information to read to a magnetometer.

The Hall Effect was discovered in 1879 by Edwin Hall while attending Johns Hopkins University for his Doctoral Degree. While a solid mathematical groundwork for electric and magnetic phenomenon had already been discovered by James Clark Maxwell, many of the physical implications and practical uses for these theories was still being explored. The interaction of magnetic and electric fields was a particularly hot topic. Hall exposed a gold leaf (metal slab) to a magnetic field perpendicular to its surface and had current flow through the slab. He observed a potential difference perpendicular to the current and also the magnetic field. This means that potential is observed not only in the direction of current flow as usual. This is what led to Hall's discovery of the Hall Effect, originally published in his paper "On a New Action of the Magnet on Electric Currents" .

Conclusion: Tips to remember

1. When a current carrying metal/conductor is placed in a magnetic field, a voltage is formed perpendicular to both current and magnetic field

2. The Hall effect is made when the charges create almost a polarized metal, as a result of being subject to a magnetic field perpendicular to the flow of electrons.

3. Right-hand rule whenever in doubt.

Hall effect can only be tested so many ways. There are a few tricks to keep in mind.

In the diagram above a voltmeter connected to a sheet of metal. Since the voltmeter reads a negative voltage, you can automatically assume that the side connected to the negative terminal of the voltmeter is connected to the positive side of the metal due to hall effect, because voltmeter is reading a charge in the opposite direction.

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Combining Electric and Magnetic Forces

Biot-Savart Law for Currents

Lorentz Force

Further reading

Books, Articles or other print media on this topic

Matter and Interactions: Volume 2 by Ruth Chabay and Bruce Sherwood (4th Edition)

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22.6 The Hall Effect

Learning objectives.

By the end of this section, you will be able to:

• Describe the Hall effect.
• Calculate the Hall emf across a current-carrying conductor.

We have seen effects of a magnetic field on free-moving charges. The magnetic field also affects charges moving in a conductor. One result is the Hall effect, which has important implications and applications.

Figure 22.26 shows what happens to charges moving through a conductor in a magnetic field. The field is perpendicular to the electron drift velocity and to the width of the conductor. Note that conventional current is to the right in both parts of the figure. In part (a), electrons carry the current and move to the left. In part (b), positive charges carry the current and move to the right. Moving electrons feel a magnetic force toward one side of the conductor, leaving a net positive charge on the other side. This separation of charge creates a voltage ε ε , known as the Hall emf , across the conductor. The creation of a voltage across a current-carrying conductor by a magnetic field is known as the Hall effect , after Edwin Hall, the American physicist who discovered it in 1879.

One very important use of the Hall effect is to determine whether positive or negative charges carries the current. Note that in Figure 22.26 (b), where positive charges carry the current, the Hall emf has the sign opposite to when negative charges carry the current. Historically, the Hall effect was used to show that electrons carry current in metals and it also shows that positive charges carry current in some semiconductors. The Hall effect is used today as a research tool to probe the movement of charges, their drift velocities and densities, and so on, in materials. In 1980, it was discovered that the Hall effect is quantized, an example of quantum behavior in a macroscopic object.

The Hall effect has other uses that range from the determination of blood flow rate to precision measurement of magnetic field strength. To examine these quantitatively, we need an expression for the Hall emf, ε ε , across a conductor. Consider the balance of forces on a moving charge in a situation where B B , v v , and l l are mutually perpendicular, such as shown in Figure 22.27 . Although the magnetic force moves negative charges to one side, they cannot build up without limit. The electric field caused by their separation opposes the magnetic force, F = qvB F = qvB , and the electric force, F e = qE F e = qE , eventually grows to equal it. That is,

Note that the electric field E E is uniform across the conductor because the magnetic field B B is uniform, as is the conductor. For a uniform electric field, the relationship between electric field and voltage is E = ε / l E = ε / l , where l l is the width of the conductor and ε ε is the Hall emf. Entering this into the last expression gives

Solving this for the Hall emf yields

where ε ε is the Hall effect voltage across a conductor of width l l through which charges move at a speed v v .

One of the most common uses of the Hall effect is in the measurement of magnetic field strength B B . Such devices, called Hall probes , can be made very small, allowing fine position mapping. Hall probes can also be made very accurate, usually accomplished by careful calibration. Another application of the Hall effect is to measure fluid flow in any fluid that has free charges (most do). (See Figure 22.28 .) A magnetic field applied perpendicular to the flow direction produces a Hall emf ε ε as shown. Note that the sign of ε ε depends not on the sign of the charges, but only on the directions of B B and v v . The magnitude of the Hall emf is ε = Blv ε = Blv , where l l is the pipe diameter, so that the average velocity v v can be determined from ε ε providing the other factors are known.

Example 22.3

Calculating the hall emf: hall effect for blood flow.

A Hall effect flow probe is placed on an artery, applying a 0.100-T magnetic field across it, in a setup similar to that in Figure 22.28 . What is the Hall emf, given the vessel’s inside diameter is 4.00 mm and the average blood velocity is 20.0 cm/s?

Because B B , v v , and l l are mutually perpendicular, the equation ε = Blv ε = Blv can be used to find ε ε .

Entering the given values for B B , v v , and l l gives

This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. ε ε is particularly difficult to measure, because there are voltages associated with heart action (ECG voltages) that are on the order of millivolts. In practice, this difficulty is overcome by applying an AC magnetic field, so that the Hall emf is AC with the same frequency. An amplifier can be very selective in picking out only the appropriate frequency, eliminating signals and noise at other frequencies.

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The hall effect.

Evolution of Resistance Concepts  |  The Hall Effect and the Lorentz Force  |  The van der Pauw Technique

Evolution of Resistance Concepts

Electrical characterization of materials evolved in three levels of understanding. In the early 1800s, the resistance R and conductance G were treated as measurable physical quantities obtainable from two-terminal I-V measurements (i.e., current I , voltage V ). Later, it became obvious that the resistance alone was not comprehensive enough since different sample shapes gave different resistance values. This led to the understanding (second level) that an intrinsic material property like resistivity (or conductivity) is required that is not influenced by the particular geometry of the sample. For the first time, this allowed scientists to quantify the current-carrying capability of the material and carry out meaningful comparisons between different materials.

By the early 1900s, it was realized that resistivity was not a fundamental material parameter, since different materials can have the same resistivity. Also, a given material might exhibit different values of resistivity, depending upon how it was synthesized. This is especially true for semiconductors, where resistivity alone could not explain all observations. Theories of electrical conduction were constructed with varying degrees of success, but until the advent of quantum mechanics, no generally acceptable solution to the problem of electrical transport was developed. This led to the definitions of carrier density n and mobility µ (third level of understanding) which are capable of dealing with even the most complex electrical measurements today.

The Hall Effect and the Lorentz Force

The basic physical principle underlying the Hall effect is the Lorentz force, which is a combination of two separate forces: the electric force and the magnetic force. When an electron moves along the electric field direction perpendicular to an applied magnetic field, it experiences a magnetic force - q v X B acting normal to both directions. The direction of this magnetic force can be determined by using the right hand rule convention. With an open hand, the fingers are pointed along the direction of the carrier velocity and curled into the direction of the magnetic field. The magnetic force direction on an electron is then determined by the opposite direction that the thumb is pointing. The resulting Lorentz force  F is therefore equal to - q ( E + v x B ) where q (1.602x10 -19 C) is the elementary charge, E is the electric field, v is the particle velocity, and B is the magnetic field. For an n -type, bar-shaped semiconductor such as that shown in Fig.1 , the carriers are predominately electrons of bulk density n . We assume that a constant current I flows along the x-axis from left to right in the presence of a z-directed magnetic field. Electrons subject to the Lorentz force initially drift away from the current direction toward the negative y-axis, resulting in an excess negative surface electrical charge on this side of the sample. This charge results in the Hall voltage, a potential drop across the two sides of the sample. (Note that the force on holes is toward the same side because of their opposite velocity and positive charge.) This transverse voltage is the Hall voltage V H and its magnitude is equal to IB/qnd , where I is the current, B is the magnetic field, d is the sample thickness, and q (1.602 x 10 -19 C) is the elementary charge. In some cases, it is convenient to use layer or sheet density ( n s = nd ) instead of bulk density. One then obtains the equation

  n s = IB /q| V H |.

Thus, by measuring the Hall voltage V H and from the known values of I , B , and q , one can determine the sheet density n s of charge carriers in semiconductors. If the measurement apparatus is set up as described later in Section IV, the Hall voltage is negative for n -type semiconductors and positive for p -type semiconductors. The sheet resistance R S of the semiconductor can be conveniently determined by use of the van der Pauw resistivity measurement technique. Since sheet resistance involves both sheet density and mobility, one can determine the Hall mobility from the equation

µ = | V H |/ R S IB = 1/( qn S R S ).

If the conducting layer thickness d is known, one can determine the bulk resistivity ( ρ = R S d ) and the bulk density ( n = n S / d ).

The van der Pauw Technique

In order to determine both the mobility µ  and the sheet density n s , a combination of a resistivity measurement and a Hall measurement is needed. We discuss here the van der Pauw technique which, due to its convenience, is widely used in the semiconductor industry to determine the resistivity of uniform samples (References 3 and 4). As originally devised by van der Pauw, one uses an arbitrarily shaped (but simply connected, i.e., no holes or nonconducting islands or inclusions), thin-plate sample containing four very small ohmic contacts placed on the periphery (preferably in the corners) of the plate. A schematic of a rectangular van der Pauw configuration is shown in Fig. 2 .

The objective of the resistivity measurement is to determine the sheet resistance R S . Van der Pauw demonstrated that there are actually two characteristic resistances R A and R B , associated with the corresponding terminals shown in Fig. 2 . R A and R B are related to the sheet resistance R S through the van der Pauw equation

exp(-π R A / R S ) + exp(-π R B / R S ) = 1

which can be solved numerically for R S .

The bulk electrical resistivity ρ can be calculated using

ρ = R S d .

To obtain the two characteristic resistances, one applies a dc current I into contact 1 and out of contact 2 and measures the voltage V 43 from contact 4 to contact 3 as shown in Fig. 2 . Next, one applies the current I into contact 2 and out of contact 3 while measuring the voltage V 14 from contact 1 to contact 4. R A and R B are calculated by means of the following expressions:

R A = V 43 / I 12 and R B = V 14 / I 23 .

The objective of the Hall measurement in the van der Pauw technique is to determine the sheet carrier density n s by measuring the Hall voltage V H . The Hall voltage measurement consists of a series of voltage measurements with a constant current I and a constant magnetic field B applied perpendicular to the plane of the sample. Conveniently, the same sample, shown again in Fig. 3 , can also be used for the Hall measurement. To measure the Hall voltage V H , a current I is forced through the opposing pair of contacts 1 and 3 and the Hall voltage V H (= V 24 ) is measured across the remaining pair of contacts 2 and 4. Once the Hall voltage V H is acquired, the sheet carrier density n s can be calculated via n s = IB / q | V H | from the known values of I , B , and q .

A second type of geometry that is sometimes used includes the parallelepiped or bridge-type sample. These may be more desirable in the case of anisotropic material properties. the restrictions on shape and size are more rigid than those of the van der Pauw specimen, but measurements can be made using either a six or an eight contact configuration. The bridge-type specimen differs from the parallelepiped in that the contacts are placed on arms that branch off the main parallelepiped base. The details of this method can be obtained from the ASTM document listed in the references.

There are practical aspects which must be considered when carrying out Hall and resistivity measurements. Primary concerns are (1) ohmic contact quality and size, (2) sample uniformity and accurate thickness determination, (3) thermomagnetic effects due to nonuniform temperature, and (4) photoconductive and photovoltaic effects which can be minimized by measuring in a dark environment. Also, the sample lateral dimensions must be large compared to the size of the contacts and the sample thickness. Finally, one must accurately measure sample temperature, magnetic field intensity, electrical current, and voltage.

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Akademgorodok 2.0 Megaproject: Are Dreams Coming True?

• INSTITUTIONAL PROBLEMS OF SPATIAL DEVELOPMENT
• Published: 07 April 2020
• Volume 10 , pages 107–116, ( 2020 )

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• V. E. Seliverstov 1  

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The development of science-oriented urban settlements in Russia—so-called naukograds and akademgorodoks—is examined against the global backdrop of the evolving regional science and innovation systems. It is concluded that the strongest among these settlements should receive state support aimed at developing national centers for the integration of science, education, and high-tech business. It is shown that Novosibirsk Akademgorodok should become such a center. Akademgorodok hosts the Novosibirsk Scientific Center (Siberian Branch, Russian Academy of Sciences), the leader among Russia’s regional science and innovation systems in terms of scale and diversification of research and development. An overview is given of the main principles of the Siberian Science Polis Strategic Initiative, proposed as part of the Program for Reindustrialization of the Economy of Novosibirsk Oblast until 2025, and the Concept for the Development of the Novosibirsk Scientific Center (Novosibirsk Akademgorodok) as a Territory with a High Concentration of Research and Development (Akademgorodok 2.0 megaproject), drafted at the direct instruction of the President of the Russian Federation. Comparative analysis of these documents yields the conclusion that they are very close conceptually, but the Akademgorodok 2.0 megaproject provides a more detailed plan for the development of a world-class science and innovation infrastructure alongside housing, social, transport, and engineering infrastructure to create a modern and comfortable social environment. Opportunities are discussed for the development of a global-scale science and education center established under the auspices of Novosibirsk State University drawing on its relationships with research institutes and industrial partners. Positive impacts are identified, as well as problematic areas and risks, of the Akademgorodok 2.0 megaproject on the development of Novosibirsk oblast and Novosibirsk.

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Academician M.A. Lavrent’ev: life experience, Nauka Sib ., 1997, no. 37.

Ivanov, V.V., Innovatsionnaya paradigma XXI (Innovative Paradigm 21st), Moscow: Nauka, 2015, 2nd ed.

Ivanov, V.V. and Matirko, V.I., Naukogrady Rossii: ot metodologii k praktike (Naukogrady–Scientific Towns of Russia: From Methodology to Practice), Moscow: Skanrus, 2001.

Kravchenko, N.A. and Markova, V.D., Multi-agent interactions in the regional innovation system, Innovatsii , 2018, no. 6, pp. 51–55.

Rubinshtein, A.Ya., Fundamental science in the focus of the state, Nezavisimaya Gazeta , 2018, Dec. 11.

Untura, G.A., Strategic partnership in scientific-technical sphere of the regions (a case study of Novosibirsk Scientific Center (Siberian Branch, Russian Academy of Sciences), Reg.: Ekon. Sotsiol ., 2018, no. 4 (100), pp. 192–227.

Khorvat, D., Regional heterogeneity of scientific-research studies in Eastern and Central Europe, Reg.: Ekon. Sotsiol ., 2009, no. 4, pp. 259–277.

Seliverstov, V., Major cities and urbanization: Russian features and the possible impact of the BRICS partnership, in The BRICS Partnership: Challenges and Prospects for Multilevel Government , Steyler, N., Ed., Cape Town: Juta, 2018, chap. 13, pp. 122–131.

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Seliverstov, V.E., Melnikova, L.V., Kolomak, E.A., Kryukov, V.A., Suslov, V.I., and Suslov, N.I., Spatial development strategy of Russia: expectations and realities, Reg. Res. Russ ., 2019, vol. 9, no. 2, pp. 155–163. https://doi.org/10.1134/S2079970519020114

Article   Google Scholar  

Seliverstov, V.E., Program for reindustrialization of the economy of Novosibirsk oblast: main outcomes of its development, Reg. Res. Russ ., 2017, vol. 7, no. 1, pp. 53–61. https://doi.org/10.1134/S2079970517010063

Seliverstov, V.E., Strategic planning and strategic errors: Russian realities and trends, Reg. Res. Russ ., 2018, vol. 8, no. 1, pp. 110–120. https://doi.org/10.1134/S2079970518010082

Setting Up, Managing and Evaluating EU Science and Technology Parks: An Advice and Guidance Report on Good Practice , Luxembourg: Publ. Off. European Union, 2014. https://www.iasp.ws/ref.aspx?id=8513&action=show.

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The article was supported in part by IEIE SB RAS, project XI.173.1.1. “Project–Program Approach in Regional Policy and in Regional Strategic Planning and Management: Methodology, Practice, Institutions.”

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Seliverstov, V.E. Akademgorodok 2.0 Megaproject: Are Dreams Coming True?. Reg. Res. Russ. 10 , 107–116 (2020). https://doi.org/10.1134/S2079970520010098

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Published : 07 April 2020

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DOI : https://doi.org/10.1134/S2079970520010098

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