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 ↓


Magnetism


Magnetism is a fundamental force of nature that is an integral part of our universe, playing a vital role in a variety of physical processes and technologies. It is one of the components of electromagnetism, one of the four fundamental forces of nature. At the undergraduate level, understanding magnetism is essential as it combines concepts ranging from classical physics to more modern ideas including quantum mechanics and relativity. Our exploration of magnetism will cover various aspects including magnetic fields, forces due to magnetic fields, sources of magnetic fields, and real-life applications of magnetism.

Understanding magnetic fields

A magnetic field is the region around a magnetic material or a moving electric charge within which the force of magnetism acts. It is invisible but can be represented through a magnetic field line diagram. The idea of a magnetic field will help in understanding how magnets exert force on each other without coming in direct contact.

The simplest and most solid source of a magnetic field is a bar magnet. A bar magnet has a north pole and a south pole. The magnetic field lines emerge from the north pole and enter from the south pole.

North Pole → -----> South Pole

In a more visual representation:


    
        
        N
        S

These blue lines in the figure represent magnetic field lines. Note that they never cross each other and form closed loops. In this case, they are outside and around the magnet, which shows how magnetic forces are applied.

Magnetic force

Magnetic forces work when a charged particle moves in a magnetic field. The force applied is perpendicular to both the direction of the particle's velocity and the magnetic field, which is defined by the cross product. The mathematical representation of the force experienced by a charged particle, known as the Lorentz force, is represented by:

F = q(v × B)
  • F is the magnetic force on the charge.
  • q is the electric charge.
  • v is the velocity of the charge.
  • B is the magnetic field vector.

Consider the scenario of a positive charge moving parallel to a magnetic field. According to the formula, since the velocity vector v is parallel to B, the cross product v × B becomes zero, indicating that no magnetic force acts on the charge. However, if the particle moves perpendicular to the field, the scenario changes:

F = qvB sin(θ)

where θ is the angle between the velocity of the particle and the magnetic field. When θ = 90°, sin(90°) = 1, and the force is at its maximum value, qvB, acting perpendicular to both v and B.

Sources of magnetic fields

In addition to permanent magnets, magnetic fields can be generated by electric currents. The relationship between electricity and magnetism is beautifully described by Ampere's law, which states that magnetic fields revolve around electric currents. Mathematically, this is represented as:

∮ B · dl = μ₀I
  • The left part is the integral of the magnetic field B around the closed path (C).
  • dl denotes an infinitesimal element of the path.
  • μ₀ is the permittivity of free space.
  • I is the current bounded by the path C.

Consider a long, straight wire carrying a current I. According to Ampere's law, the magnetic field produced at a distance r from the wire is given by:

B = (μ₀I) / (2πr)

The field lines form concentric circles around the wire, and their direction follows the right-hand rule: if you place your right thumb in the direction of the current, your fingers bend in the direction of the magnetic field.

The loop current method of creating magnetic fields can be extended to coils or solenoids, where a long coil of wire with current produces a approximately uniform magnetic field within the coil and a complex field outside.


    
        
        
        
        
        Current(I)

Earth's magnetic field

Interestingly, our planet Earth acts like a giant magnet whose magnetic field extends from the North Pole to the South Pole. This field protects the Earth from cosmic and solar winds. The compass works based on the Earth's magnetic field, where the needle aligns itself with the Earth's magnetic north and south poles.

Applications of magnetism

Magnetism has many applications in modern technology. Here are some examples:

  • Magnetic storage: Devices such as hard drives use magnetic fields to store data.
  • Electric motors: use magnetic forces to convert electrical energy into mechanical energy.
  • Magnetic resonance imaging (MRI): Used in medical imaging to create detailed images of the body's organs and tissues.
  • Transformers: Rely on electromagnetic induction to transfer energy between circuits.

In conclusion, magnetism is not only a fundamental phenomenon but also a versatile tool in technology and research. It is like a bridge in physics, leading to more advanced topics and practical applications in many fields, including engineering, medicine, and communications.


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Magnetism

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