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


Electromagnetism is a branch of physics that studies the interactions between electric charges and magnetic fields. It explains a wide range of physical phenomena and is fundamental to understanding how many everyday technologies work, from motors to light bulbs and mobile phones. The subject is crucial to the development of various technologies and plays a vital role in our understanding of the universe.

Basic concepts

To understand the concepts of electromagnetism, it is necessary to start with the basic definitions of electric charge, electric field, magnetic field and electromagnetic force. Let us understand each of these concepts in detail.

Electric charge

Electric charge is a fundamental property of matter. There are two types of electric charge: positive and negative. Like charges repel each other, and unlike charges attract each other. The net charge of an object is determined by the balance between positive (protons) and negative (electrons) charges.

An everyday example of electric charge is static electricity. When you rub a balloon on your hair, the electric charge transferred between your hair and the balloon can cause it to stick to the wall.

Electric field

An electric field is the region around a charged object where other charges experience a force. The strength and direction of the electric field is represented by electric field lines that emanate from positive charges and converge at negative charges.

The electric field E at any point in space can be defined using the following formula:

E = F/q

where F is the force acting on a small positive test charge q.

Visual example: electric field

Here is a simple representation of electric field lines around positive and negative charges:

+-

Magnetic field

The magnetic field is produced by moving electric charges, such as electric current, and is represented by magnetic field lines. These lines form closed loops and never begin or end at a point. The direction of the magnetic field is tangent to the field lines.

The Earth's magnetic field is a typical example that we experience every day. Compasses use this to indicate north.

Electromagnetic force

The electromagnetic force is a combination of electric and magnetic forces on a charged particle due to electromagnetic fields. This fundamental interaction occurs between particles that carry electric charge.

The force F experienced by a charge q moving with velocity v in a magnetic field B is given by the Lorentz force equation:

F = q(E + v × B)

where × denotes the cross product.

Electromagnetic waves

Electromagnetic waves are waves that have both electric and magnetic field components. They propagate through space at the speed of light and do not require any medium to travel.

Examples of electromagnetic waves include visible light, radio waves, and X-rays. These waves are fundamental in telecommunications, medical imaging, and more.

Visual example: electromagnetic wave

Maxwell's equations

Maxwell's equations are a set of four electromagnetic field equations that are fundamental to classical electromagnetism, classical optics, and electrical circuits. These equations describe how electric and magnetic fields interact and propagate.

Gauss's law

Gauss's law relates the electric flux passing through a closed surface to the charge enclosed by that surface. Mathematically, it can be written as:

∮ E · dA = Q/ε₀

Where ∮ denotes the surface integral, E is the electric field, dA is the differential area on a closed surface, Q is the total charge enclosed, and ε₀ is the permittivity of free space.

Faraday's law of induction

Faraday's law describes how a time-varying magnetic field can produce an electromotive force (emf) in a closed loop. The formula is:

emf = -dΦB/dt

Where ΦB is the magnetic flux. The negative sign indicates the direction of the induced emf according to Lenz's law.

Ampere's law with Maxwell's addition

It describes the changes in the magnetic field and electric field associated with a transverse electric current. It is given as:

∮ B · dl = μ₀(I + ε₀ dΦE/dt)

Where ∮ indicates a linear integral, B is the magnetic field, dl is the differential length, μ₀ is the permeability of free space, and ΦE is the electric flux.

Gauss's law for magnetism

Gauss's law for magnetism states that the net magnetic flux flowing out of any closed surface is zero. This means that there are no magnetic monopoles. It can be expressed as:

∮ B · dA = 0

Applications of electromagnetism

Electrical motors

Electric motors use electromagnetism to convert electrical energy into mechanical energy. The interaction between the magnetic field and the current in the windings creates a force, causing the rotor to spin.

Transformers

Transformers are devices that use electromagnetic induction to change the voltage level of alternating current (AC) in power systems. They allow us to distribute electrical power efficiently over long distances.

Electric generator

Generators convert mechanical energy into electrical energy using electromagnetism, usually by rotating a coil in a magnetic field or vice versa.

Magnetic resonance imaging (MRI)

MRI is a medical imaging technique that uses strong magnetic fields and radio waves to make pictures of body organs. It takes advantage of the principles of nuclear magnetic resonance.

In short, electromagnetism is fundamental to our modern technology and understanding of physical phenomena. By examining examples such as electric motors, generators, and MRIs, we see its important role in a variety of applications. Fundamental laws such as Maxwell's equations provide the mathematical framework to effectively describe these electromagnetic interactions.


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Electromagnetism

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