22.6 The Hall Effect
3 min read•june 18, 2024
The occurs when a acts on a current-carrying conductor, creating a voltage across it. This phenomenon reveals crucial info about in materials, helping us understand their electrical properties and behavior.
Scientists and engineers use the to measure magnetic fields, determine charge carrier types, and develop sensors. It's a powerful tool for studying and applying electrical conductivity in various materials, from to metals.
The Hall Effect
Hall effect voltage creation
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- Current-carrying conductor placed in perpendicular magnetic field experiences transverse on charge carriers given by where is charge, is velocity, and is magnetic field ()
- deflects charge carriers to one side of conductor creating charge imbalance with positive charge carriers () accumulating on one side and negative charge carriers () on opposite side
- Charge imbalance generates transverse () within conductor that opposes Lorentz force until equilibrium reached when forces balanced
- Resulting potential difference across conductor is () caused by Hall
Hall voltage calculation formula
- Hall voltage () calculated using equation where is magnetic field strength in teslas (T), is conductor width in meters (m), and is of charge carriers in meters per second (m/s)
- () calculated using equation where:
- is current in amperes (A)
- is charge carrier density in carriers per cubic meter (m)
- is charge of carriers in coulombs (C)
- is cross-sectional area of conductor in square meters (m)
- Sign of Hall voltage depends on type of charge carriers with positive for holes and negative for
Hall effect practical applications
- Determining charge carrier type based on sign of Hall voltage
- Positive Hall voltage indicates majority charge carriers are positive (holes) as in ()
- Negative Hall voltage indicates majority charge carriers are negative (electrons) as in ()
- Measuring magnetic field strength by calculating from measured Hall voltage, known current, conductor width, and charge carrier density
- used to measure magnetic fields, current, or position in applications like automotive systems (wheel speed sensors), industrial control (proximity switches), and consumer electronics (smartphone compasses)
- Studying material electrical properties such as conductivity, carrier density, and mobility valuable for characterizing and developing new materials especially semiconductors ()
Additional Hall effect parameters
- (R_H) relates Hall electric field to current density and magnetic field, providing information about charge carrier type and density
- (μ) describes how quickly charge carriers move through a material in response to an electric field, affecting conductivity
- (ρ_H) represents the transverse resistivity induced by the Hall effect, related to the Hall coefficient and magnetic field
- is the change in electrical resistance of a material when exposed to a magnetic field, often studied alongside the Hall effect
Key Terms to Review (32)
Charge Carrier Mobility: Charge carrier mobility is a measure of how quickly charged particles, such as electrons and holes, can move through a material under the influence of an electric field. It is a crucial parameter in understanding the electrical properties and performance of semiconductor devices.
Charge Carriers: Charge carriers are the mobile, electrically charged particles that are responsible for the flow of electric current in a material. These charge carriers can be either positively or negatively charged and are the fundamental building blocks of electrical phenomena.
Coulomb: Coulomb is the fundamental unit of electric charge, named after the French physicist Charles-Augustin de Coulomb. It is a measure of the amount of electric charge and is a crucial concept in understanding various topics in electricity and magnetism, such as static electricity, electric fields, electric potential, and the behavior of charged particles.
Coulomb force: Coulomb force, also known as the electrostatic force, is the force of attraction or repulsion between two charged particles. It follows an inverse-square law and is governed by Coulomb's law.
Drift velocity: Drift velocity is the average velocity at which free charge carriers, such as electrons, move through a conductor under the influence of an electric field. It is typically much smaller than the speed of individual electrons due to frequent collisions within the material.
Drift Velocity: Drift velocity is the average velocity at which charge carriers, such as electrons or holes, move through a material under the influence of an applied electric field. It is a fundamental concept in understanding the flow of electric current and the behavior of electrical devices.
Electric and magnetic fields: Electric and magnetic fields are two interdependent fields that propagate as waves through space. They form the basis of electromagnetic waves, where oscillations in one field induce oscillations in the other.
Electric Field: The electric field is a vector field that describes the force experienced by a stationary, positive test charge at any given point in space. It represents the strength and direction of the electric force exerted on a charged particle by other charges in the vicinity, and is a fundamental concept in the study of electromagnetism and the behavior of charged particles.
Electrons: Electrons are subatomic particles with a negative electric charge, symbolized as $e^{-}$. Found in all atoms, they play a crucial role in electricity and chemical bonding.
Electrons: Electrons are subatomic particles that carry a negative electric charge and are found in all atoms, orbiting the nucleus. They play a crucial role in the fundamental forces and interactions that govern the behavior of matter and energy in the universe.
Gallium Arsenide: Gallium arsenide (GaAs) is a compound semiconductor material composed of gallium and arsenic. It is widely used in the electronics and optoelectronics industries due to its unique electronic and optical properties, making it a crucial material in various applications, particularly in the context of the Hall Effect.
Germanium: Germanium is a chemical element with the symbol Ge and atomic number 32. It is a hard, grayish-white metalloid that is chemically similar to silicon, its group-IV neighbor on the periodic table. Germanium's unique electronic properties make it a crucial material in various electronic and optical applications, particularly in the context of the Hall Effect.
Hall Coefficient: The Hall coefficient is a material property that describes the response of a conductor or semiconductor to a magnetic field. It is a measure of the voltage developed across a material perpendicular to both the direction of an electric current and an applied magnetic field, and is used to determine the sign and density of charge carriers in the material.
Hall effect: The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor when a magnetic field is applied perpendicular to the current. It demonstrates the nature of charge carriers in a conductor.
Hall Effect: The Hall effect is a phenomenon in which a voltage difference is produced across an electrical conductor transverse to an electric current in the conductor and a magnetic field perpendicular to the current. This effect is widely used in various applications, including magnetic field sensors, current sensors, and Hall-effect switches.
Hall effect sensors: Hall effect sensors are devices that detect the presence and strength of a magnetic field through the Hall effect, which is the generation of a voltage across a conductor when it is placed in a magnetic field. These sensors play a critical role in various applications, from automotive to industrial, by converting magnetic energy into electrical signals, enabling precise measurements and control.
Hall Electric Field: The Hall electric field is a voltage difference that develops transverse to both the direction of the current flow and the applied magnetic field in a conductor or semiconductor material. This effect is known as the Hall effect and is used to measure the strength of magnetic fields and to determine the charge carrier type and concentration in materials.
Hall emf: Hall emf is the voltage difference generated across an electrical conductor through which an electric current is flowing, due to the presence of a perpendicular magnetic field. It is a direct consequence of the Hall Effect.
Hall Resistivity: Hall resistivity is a physical phenomenon that occurs when a current-carrying conductor is placed in a magnetic field. It arises due to the deflection of charge carriers, such as electrons, by the magnetic field, resulting in the development of a potential difference perpendicular to both the current and the magnetic field.
Hall Voltage: Hall voltage is an electrical potential difference that is generated perpendicular to both the direction of an electric current flowing through a conductor and an applied magnetic field. This phenomenon is known as the Hall effect and has important applications in various electronic devices and sensors.
Holes: In solid-state physics, holes refer to the absence of an electron in a semiconductor material, acting as positive charge carriers. When an electron leaves its position in the atomic lattice, it creates a 'hole' that can move through the material, effectively allowing for electrical conduction. Holes play a crucial role in understanding the behavior of semiconductors, influencing their electrical properties and the design of electronic devices.
Lorentz force: The Lorentz force is the force experienced by a charged particle moving through an electric and magnetic field. It is given by the equation $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $q$ is the charge, $\mathbf{E}$ is the electric field, $\mathbf{v}$ is the velocity of the particle, and $\mathbf{B}$ is the magnetic field.
Lorentz Force: The Lorentz force is the force exerted on a moving charged particle when it is placed in a magnetic field. It is a fundamental concept in electromagnetism that describes the interaction between electric and magnetic fields and the motion of charged particles.
Magnetic Field: A magnetic field is a region in space where magnetic forces can be detected. It is a vector field that describes the magnetic influence of electric currents and magnetized materials on the space around them. The magnetic field is a fundamental concept in electromagnetism and is essential for understanding various phenomena in physics, including the behavior of ferromagnets, the motion of charged particles, and the production of electromagnetic waves.
Magnetic Flux Density: Magnetic flux density, also known as magnetic induction or magnetic field strength, is a measure of the strength of a magnetic field. It quantifies the amount of magnetic flux per unit area perpendicular to the direction of the field. This term is crucial in understanding various electromagnetic phenomena, including the force on a moving charge, the Hall effect, the magnetic force between parallel conductors, motional electromotive force (emf), and eddy currents.
Magnetoresistance: Magnetoresistance is the property of a material to change its electrical resistance in the presence of an external magnetic field. This phenomenon is observed in various materials and has important applications in the field of electronics and magnetic sensing.
N-type Semiconductors: n-type semiconductors are a type of semiconductor material that has been doped with impurities to create an excess of free electrons, making them n-type (negative-type). This excess of electrons allows for the efficient conduction of electric current, making n-type semiconductors a crucial component in various electronic devices and circuits.
P-type Semiconductors: p-type semiconductors are a type of semiconductor material that has an excess of positive charge carriers, known as holes, rather than free electrons. This is achieved by doping the semiconductor, typically silicon or germanium, with impurities that have one less valence electron than the host atoms.
Semiconductors: Semiconductors are materials that have electrical conductivity properties that fall between those of conductors and insulators. They can be used to control and amplify the flow of electric current, making them essential components in modern electronic devices and technologies.
Silicon: Silicon is a chemical element that is a metalloid, meaning it has properties of both metals and nonmetals. It is the second most abundant element in the Earth's crust after oxygen and is a critical component in the semiconductor industry, being the primary material used in the manufacture of computer chips and other electronic devices.
Tesla: The tesla (T) is the SI unit of magnetic field strength or magnetic flux density. It measures how much force a magnetic field exerts on moving charges or current-carrying wires.
Tesla: The tesla (T) is the unit of magnetic flux density or magnetic induction in the International System of Units (SI). It is named after the Serbian-American inventor and electrical engineer Nikola Tesla, who made significant contributions to the design of the modern alternating-current (AC) electrical supply system.