Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Solid state physics → Electrical and Magnetic Properties ↓


Hall effect


The Hall effect is an important phenomenon in solid state physics and is helpful in understanding the behaviour of electrically charged particles in various materials. Named after Edwin Hall, who discovered it in 1879, the Hall effect forms the basis for determining the nature of charge carriers in semiconductors and helps in the development of many technologies, including sensors and transducers.

Basic principle of the Hall effect

The Hall effect can be observed when a magnetic field is applied perpendicular to the flow of electric current through a conductor. As charged particles (usually electrons) move through the conductor, they experience a force due to the magnetic field, known as the Lorentz force. This force deflects the particles toward one side of the conductor, creating a potential difference (voltage) across the conductor. This voltage is perpendicular to the direction of both the original current and the magnetic field.

The structure of the Hall effect setup can be understood through the following equation:

V_H = (B * I) / (n * e * d)

Where,

  • V_H is the Hall voltage.
  • B is the magnetic field strength.
  • I is the current flowing through the conductor.
  • n is the charge carrier density (number of charge carriers per unit volume).
  • e is the fundamental charge (charge of the electron).
  • d is the thickness of the conductor.

Visualization example

To understand the Hall effect consider the following simple example:

B I V H

in this view:

  • The rectangle represents a good conductor material.
  • The vertical line and label B represent the magnetic field applied perpendicular to the surface.
  • The horizontal line and the label I represent the current flowing through the material.
  • The small circle represents the deflection of charge carriers (electrons) due to the magnetic field.
  • The label V H (Hall voltage) appears at the edges where the potential difference is measurable.

Derivation and explanation

Consider a plane rectangular conductor carrying current and an applied magnetic field perpendicular to the current flow. The deflection of charge carriers (usually electrons) due to the magnetic field causes charge separation across the width of the conductor, producing a transverse voltage called the Hall voltage.

The Lorentz force acting on a charged particle can be described by the following equation:

F = q * (v × B)

Where:

  • F is the force acting on the charge particle.
  • q is the charge of the particle.
  • v is the velocity of the charge carrier.
  • B is the strength of the magnetic field.

For electrons, the force will cause a deflection to one side of the conductor, setting up an electric field (E) perpendicular to both I and B. The magnitude of this electric field can be given by the Hall voltage over the width of the material:

E = V_H / w

Applications of Hall effect

  • Magnetic field sensors: Hall sensors are widely used in devices that measure the magnitude of magnetic fields. This includes systems in automotive, aerospace, and consumer electronics.
  • Position and speed detection: Hall effect sensors are often used in brushless DC motors to accurately detect the position of the motor's rotor.
  • Switches: Hall effect sensors provide contactless switching and are used in various devices to achieve longevity and reliability by reducing wear and tear.
  • Automotive applications: In cars, Hall effect sensors help in anti-lock braking systems, speedometers, and other automotive systems that require accurate speed detection.

Important features of the Hall effect

The Hall effect offers specific advantages and characteristics, making it suitable for many technological applications:

  • Contactless measurement: By using a magnetic field, the Hall Effect provides contactless measurement, ensuring that delicate parts do not wear out over time.
  • High reliability: Hall effect sensors are robust and able to operate even under harsh conditions, where conventional mechanical sensors may fail.
  • Wide temperature range: Hall effect devices operate effectively over a wide range of temperatures, making them versatile for uses ranging from consumer gadgets to industrial machinery.
  • Miniaturization: With advances in semiconductor technology, Hall effect sensors can be made extremely small, saving space in compact electronic devices.

Conclusion

The Hall effect is a profound physical phenomenon that has widespread implications in solid state physics and many technological applications. From identifying charge carrier density to playing a key role in modern-day sensors and industrial technology, the Hall effect remains an integral part of our understanding of electronic properties in materials. Its principles form the foundation of many devices and systems that we rely on in our daily lives.


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Hall effect

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