Hall Effect: Theory, Formula & Applications

Hall Effect is a physical phenomenon that is observed when a magnetic Field is applied to a conductor. It was first discovered by American physicist Edwin Hall in 1879. 

• The Hall Effect can be used to measure the strength and direction of a magnetic field, and it has many practical applications in modern technology, including in electronic devices such as sensors and motors.
• The Hall Effect was observed when a current-carrying conductor is placed in a magnetic field that is perpendicular to the direction of the Electric Current flow. 
• The Magnetic Field causes the Electron in the conductor to be deflected to one side of the conductor, resulting in a buildup of charge on that side of the conductor. 
• Hall Effect has many practical applications in modern technology. 
• It is used in Electric motor to provide feedback on the position and speed of the rotor, and in electronic compasses to determine the orientation of a device relative to the Earth's magnetic field.

Key Terms: Hall Voltage, Lorentz Force, Hall Coefficient, Hall Effect, Magnetic Field, Hall Heroult Effect, Automotive Application 

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What is Hall Effect?

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Hall Effect is a process in which a magnetic field applied perpendicular to a current-carrying conductor induces a voltage difference perpendicular to both the magnetic field and the current. 

• In the Hall Effect When an electric current is passed through a conductor, such as a metal wire or a semiconductor, the flow of electrons creates a magnetic field around the wire.
• If an external magnetic field is applied perpendicular to the current, the electrons experience a force that deflects them to one side of the conductor. 
• This separation of charges creates a measurable voltage difference across the conductor perpendicular to both the current and the magnetic field.

Hall Effect

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Principle of Hall Effect

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According to the Hall Effect concept, a voltage may be measured at a right angle to the current route when a current-carrying conductor or semiconductor is exposed to a perpendicular magnetic field. 

Working of The Hall Effect 

The working of the Hall Effect is as follows: 

• When a current begins to flow when a conductive plate is connected to an Electric Circuit containing a battery. 
• From one end to the other, the charge carriers will move in a straight line, as a result of which magnetic fields are created. 
• The magnetic field of the charge carriers is altered when a magnet is brought close to the plate and the charge carriers' direct passage is disrupted. 
• The Lorentz Force is the force that alters the direction in which charge carriers flow. 
• Due to Faraday's Law, the magnetic field created by this motion of the magnetic charge is perpendicular to the current and creates a tangential magnetic field. 
• Positively charged holes are diverted to one side of the plate and negatively charged electrons to the other due to the distortion in the charge carriers' Magnetic Fields.

Two factors can be used to characterize the Hall Effect:

• The electric current flowing through a current-carrying wire (the input).
• The conductor's magnetic field (the input), as well as one observable variable, the Hall voltage that forms across a Hall plate (the output).

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Electromagnetic Effect

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The Electromagnetic Effect, refers to the interaction between electric and magnetic fields. An electric field produces a magnetic field, and a changing magnetic field produces an electric field. This is also known as Electromagnetic Induction and is the basis for many electrical devices, including transformers, motors, and generators.

•  The Electromagnetic Effect is responsible for the creation of the magnetic field that causes the electrons to move to one side of the conductor. 
• The current flowing through the conductor creates an electric field, which in turn produces a magnetic field. 
• This magnetic field interacts with the applied magnetic field, causing the electrons to deflect to one side of the conductor.
• The Electromagnetic Effect is responsible for the creation of the magnetic field that causes the Hall Effect to occur.

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Magnetic Field

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Magnetic Field is required to produce a voltage across a conductor. When a current-carrying conductor is placed in a magnetic field, the magnetic force acts on the free electrons in the conductor, causing them to deflect to one side of the conductor.

• As the electrons move to one side of the conductor, they create a voltage difference between the two sides of the conductor. 
• This Voltage Difference is known as the Hall voltage and is proportional to the strength of the magnetic field, the current flowing through the conductor, and the geometry of the conductor.
• The direction of the Hall voltage is perpendicular to both the direction of the magnetic field and the direction of the current flowing through the conductor which can be detected through the Right-hand thumb rule.
• The strength of the magnetic field can be measured by the Hall effect by measuring the Hall voltage across the conductor. 

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Electronic Effect

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The Electronic Effect is the effect that occurs when an electric current is passed through a conductor placed in a magnetic field.

• The Electronic Effect in the Hall effect is the result of the Motion of charged particles, specifically electrons, in a magnetic field. 
• The electrons move through the magnetic field, they experience a force perpendicular to both the direction of the magnetic field and the direction of the current. 
• This force, known as the Lorentz Force, causes the electrons to deflect to one side of the conductor, resulting in a potential difference across the conductor.
• When an electron moves through a magnetic field, it experiences a torque due to its magnetic moment, which causes it to deflect.
• The electronic effect in the Hall effect is used in a wide range of applications, such as magnetic sensors, current sensors, and position sensors. 

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Hall Voltage

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Due to the electrical charges of the current, when an electric current flows through a conductor, it creates an electrostatic field everywhere around the conductor.

• A potential difference across the conductor is produced by the charges of the current.
• A Hall Voltage is formed across the conductor and is measured as the output if it consists of one or more conductors carrying currents in the same direction.

The Hall voltage represented as VH is given by the formula:

V_H= - \(\frac{IB}{qnd}\)

Here

• 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.

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Hall Coefficient

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The Hall coefficient RH is mathematically expressed as

R_H= \(\frac{E}{jB}\)

Here, 

• j is the current density of the carrier electron.
• E is the induced Electric Field.
• B is the magnetic strength.

If there are more positive charges than negative charges, the hall coefficient is positive. The opposite is true when there are more electrons than holes.

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Derivation of Hall Effect

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The Derivation of Hall Effect can be expressed mathematically as follows: 

Consider a metal in steady-state with no movement of charges in the y-axis direction and one sort of charge carrier, electrons. 

eE_H= Bev\(\frac{eV_H}{d}\)= BevV_H = Bvd

Here,

• VH is Hall Voltage,
• EH is Hall Field,
• v is drift velocity,
• d is the width of the metal,
• B is the magnetic field,
• Bev is a force acting on an electron.

In a state of equilibrium, the magnetic field's downward force equals the electric field's upward force. 

I= -nevA

Here

• I is an Electric Current,
• n is no. of electrons per unit volume,
• A is the cross-sectional area of the conductor.

VH= - \(\frac{BI}{net}\)

The relationship between the induced electric field and the product of the current density and magnetic field is implied by the Hall coefficient (RH).

R_H= \(\frac{E_H}{jB}\) = - \(\frac{1}{ne}\)

µ_H= \(\frac{v}{E}\) = \(\frac{J}{neE}\) = σR_H = \(\frac{R_H}{ρ}\)v

Here,

• E is an electric field,
• v is the drift velocity,
• RH is the Hall coefficient,
• H is the mobility of the hole.

\(\frac{J_y}{J_x}\)= σ\(\frac{E_y}{J_z}\) = µ_HB_z = σR_HB_z

The Hall Angle, which measures the average number of radians brought on by particle collisions, is the ratio between density (in the x-axis direction) and current density (in the y-axis direction).

R= \(\frac{V_h}{i}\) = \(\frac{B}{net}\)

Here, R is Hall Resistance.

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Applications of Hall Effect

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The following list outlines the range of practical applications that Hall effect derivation has:

• Hall Effect is a type of Magnetometer since it aids in determining the magnetic field surrounding an electrical charge.
• The Hall Effect formula makes it possible to identify if a substance is an Electrical Insulators or a semiconductor.

Semiconductor Hall Devices 

The potential and current in a circuit are measured using Hall Devices. This is helpful for a variety of purposes, including the testing and design of integrated circuits. 

Hall Effect Sensors 

These are tiny solid-state Semiconductor Devices used in electrical, aeronautical, and automotive sensing and for measuring magnetic fields, including the Earth's magnetic field. For usage in tiny appliances like microwave ovens etc, hall sensors are also a well-liked substitute for reed switches.

Magneto-Resistivity and Magnetoelectric Effect 

Electrons can freely migrate between points in a metallic conductor which can be polarized by the Magnetic Field because of its mobility. 

• A Hall voltmeter can detect the change in conductor resistance brought on by the passage of electrons which can affect the strength and direction of the electric field.
•  In this effect, the direction and intensity of the magnetic field affect the conductor's resistivity and resistance magnitude.

Electro-Conductive Materials for Electromagnetic Measurement 

The Hall Effect may be used to evaluate the surface conductivity and resistivity of non-metallic materials since it can monitor the electric field. 

• Metallic materials lack the magnetic field necessary to produce an electromotive force, although metallic wires may still carry electricity. 
• Because the voltage is inversely proportional to the intensity of the electric field, high-resolution Hall voltmeters have been made possible.

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Things to Remember

• The Hall Effect is a natural process that occurs when a magnetic field is applied perpendicular to a current-carrying conductor
• It was discovered by American physicist Edwin Hall in 1879.
• The Hall Effect occurs in conductors such as metals, semiconductors, and even some liquids.
•  Magnetic field is applied perpendicular to a current-carrying conductor, and a voltage is generated in the transverse direction (i.e., perpendicular to both the current and magnetic field directions) known as the Hall voltage.
• The Hall Effect is used in a variety of applications, such as sensing magnetic fields, measuring magnetic properties of materials, and in electronic devices such as Hall effect sensors.
• The Hall Effect can be used to determine the sign (positive or negative) and density of charge carriers in a conductor, useful for studying the electrical properties of materials.
• The Hall Coefficient, which is the ratio of the Hall voltage to the product of the current and magnetic field strength.