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 → Electromagnetism → Electromagnetic induction ↓


Lenz's law


Lenz's law is a fundamental principle in electromagnetism, a branch of physics that deals with the interaction of electric and magnetic fields. It is named after German physicist Heinrich Lenz, who formulated it in 1834. Lenz's law relates the direction of the induced electromotive force (emf) and current produced by a change in magnetic flux. This law is essential to understanding electromagnetic induction, the process of producing electric current from a magnetic field. Lenz's law is formulated simply in this context: the direction of the induced current will be such that it opposes the change in magnetic flux that produced it.

Understanding the foundation

To properly understand Lenz's law, it is important to first understand the concept of magnetic flux and electromagnetic induction. Magnetic flux is a measure of the number of magnetic field lines passing through a given surface area. It is mathematically defined as:

Φ = B * A * cos(θ)

Where Φ is the magnetic flux, B is the magnetic field strength, A is the area through which the field lines pass, and θ is the angle between the field lines and the normal to the surface.

Electromagnetic induction refers to the production of electromotive force (emf) on a conductor when it is exposed to a changing magnetic field. Faraday's law of induction, discovered by Michael Faraday, quantifies this process. It states that the induced emf in any closed circuit is equal to the rate of change of magnetic flux through the circuit.

Statement of Lenz's law

Lenz's law furthers Faraday's discovery by determining the direction of the induced current. Lenz's law is stated as follows:

The direction of the induced electromotive force and current in a closed circuit is such that it opposes the change in magnetic flux that produces it.

Example: moving magnet

To understand Lenz's law better, let's imagine an example. Imagine a bar magnet moving toward a loop of conducting wire. As the magnet approaches, the magnetic flux through the loop increases.

N S moving magnet

According to Lenz's law, the induced current in the loop creates a magnetic field that opposes the increase in magnetic flux. The loop then acts like a magnet with its own pole opposite to the adjacent pole of the bar magnet. If the north pole of the magnet is moving toward the loop, the loop induces a current that creates a north pole on the nearest side to repel the adjacent magnet.

Mathematical formulation of Lenz's law

Lenz's law is naturally included in Faraday's law of induction through the negative sign.

ε = -dΦ/dt

In this formula, ε stands for the induced emf, and -dΦ/dt represents the rate of change of magnetic flux. The negative sign is the mathematical expression of Lenz's law, which shows that the induced emf is in the opposite direction of the change in magnetic flux.

Another example: changing the region

Consider a loop of wire with a changing area located in a uniform magnetic field. When the area of the loop changes, the magnetic flux changes accordingly. If the area of the loop increases, Lenz's law predicts that the induced current will flow in a direction that produces a magnetic field opposite to the increase.

Growing area

Lenz's law in everyday phenomena

While theoretical examples help clarify concepts, Lenz's law is observable in many real-world situations:

  • Induction Cookstove: In induction cooking, the cookware acts like a loop, and the changing magnetic field generated by the cooktop induces eddy currents within the cookware. These currents heat the cookware directly due to resistance.
  • Magnetic braking in trains: Some trains use the principle of electromagnetic induction for braking. When powerful magnets are alternately rotated against the metal rails or wheels, eddy currents are formed and create a magnetic field opposite to the motion, slowing down the train.
  • Electric guitar: Pickups in electric guitars use Lenz's law to convert string vibrations into electrical signals. The movement of the string changes the magnetic field, inducing a current in the coil, which is then amplified to produce sound.

Conceptual visualization: Eddy currents

Eddy currents provide another interesting application of Lenz's law. These are loops of electric currents induced within a conductor by a changing magnetic field. They can create significant electrical resistance, causing the material to heat up.

Conductor

Lenz's law and conservation of energy

Lenz's law is closely linked to the law of conservation of energy. By opposing changes in magnetic flux, it ensures that energy is conserved. Work done to change the magnetic flux, such as moving a magnet toward a coil, is converted into electrical energy in the coil.

Conclusion

Lenz's law is a cornerstone of electromagnetic theory, providing information about the behavior of circuits and materials in changing magnetic fields. By opposing changes in magnetic fields, it ensures the conservation of energy and provides practical applications in many technologies and everyday devices. Understanding Lenz's law equips us with an important perspective on the interaction between electricity and magnetism in the physical world.


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Lenz's law

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