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 ↓


Magnetic Fields and Forces


Magnetism is a fascinating part of physics that plays a vital role in our everyday lives. We encounter various aspects of magnetism in many technology-based applications, such as motors, generators, magnetic storage, and more. Understanding the principles of magnetic fields and forces can help you appreciate the power and potential of this phenomenon.

Introduction to Magnetism

Magnetism is a fundamental aspect of electromagnetism, one of the four fundamental forces of nature. At its core, magnetism arises from the movement of electric charges. All materials exhibit some form of magnetic behavior, but it is most commonly seen in ferromagnetic materials such as iron, cobalt, and nickel.

Magnetic Field

A magnetic field is a region in space where magnetic force can be detected. It is created by moving electric charges, such as in a current-carrying wire, or by the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property called spin. The symbol B is used to represent magnetic fields, and they are measured in teslas (T).

B-field direction

The direction of the magnetic field at any point is the direction in which the north monopole would move if placed at that point. Unfortunately, magnetic monopoles are not isolated objects, but instead serve as an excellent conceptual tool for understanding fields.

Magnetic field visualization

Magnetic fields can be visualized using magnetic field lines. These imaginary lines flow from the north pole of a magnet to the south pole. They never cross each other, and the denser the lines are, the stronger the magnetic field.

N S

Magnetic force

Magnetic force is the force experienced in a magnetic field. It appears in two main forms:

  1. The force acting on a moving charge in a magnetic field.
  2. The force between two current carrying wires.

Force on a moving charge

When a charged particle passes through a magnetic field, it experiences a force called the Lorentz force. The magnitude of the force is determined by the following equation:

F = q(v × B)

Where:

  • F is the magnetic force in newtons (N).
  • q is the charge in coulombs (C).
  • v is the velocity of the charge in meters per second (m/s).
  • B is the magnetic field strength in Tesla (T).
  • × denotes the vector cross product.
V B Why

The Lorentz force is perpendicular to both the velocity of the charge and the external magnetic field. Because of this perpendicular relationship, magnetic forces do not do work on charged particles, and thus they cannot change the kinetic energy of the particles, only their direction.

A practical example is charged particles in cyclotron accelerators, where high speeds are achieved by particles moving in circular paths under extremely strong magnetic fields.

Force between current carrying wires

Two parallel wires carrying current will exert a magnetic force on each other. The direction of the force depends on the direction of the current in the wires:

  • If the currents are in the same direction the wires attract each other.
  • If the currents flow in opposite directions, the wires repel each other.

The force per unit length between two parallel wires is given by:

F/L = (μ0 /2π) × (I1 I2 /d)

Where:

  • F/L is the force per unit length in newtons per metre (N/m).
  • μ0 is the permittivity of free space, approximately 4π × 10-7 T·m/A.
  • I1 and I2 are currents in amperes (A).
  • d is the distance between the wires in meters.
I1 I2 D

This principle forms the basis for defining the unit of electric current, the ampere.

Conclusion

Understanding magnetic fields and forces is essential to understanding electromagnetic phenomena and their applications in technology. From determining the trajectories of charged particles to predicting interactions between current-carrying wires, the study of magnetism is rich in concepts and applications that extend to both theoretical physics and practical engineering. Through the exploration of magnetic fields and forces, we gain insight into one of the most intriguing forces of the natural world, leading to innovations that shape our technological landscape.

By mastering this subject, you will lay the foundation for in-depth study of electromagnetic principles and their practical implementation, and inspire the next wave of advances in scientific research and engineering design.


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Magnetic Fields and Forces

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