Ampère's Law

This lecture covers the derivation of Maxwell's equations, focusing on the need for an equation to describe time-varying fields and the relationship between magnetic field B and current distribution. It then delves into Ampère's circuital law, illustrating its equivalence to Bio-Savart's law and its application in systems with high symmetry. The lecture emphasizes the importance of identifying symmetry, choosing appropriate integration paths, and determining enclosed current. Practical examples and calculations are provided to demonstrate the application of Ampère's law.

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PHYS-114: General physics: electromagnetism

The course first develops the basic laws of electricity and magnetism and illustrates the use in understanding various electromagnetic phenomena.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Symmetry

Symmetry () in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Maxwell's equations in curved spacetime

In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may not be the Minkowski metric) or where one uses an arbitrary (not necessarily Cartesian) coordinate system. These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime.

Electromagnetic field

An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.

Earth's magnetic field

Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of a mixture of molten iron and nickel in Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo.

Magnetic Field and Ampere's Law

Explores magnetic fields, Ampère's law, and electromagnetic circuits, covering topics such as magnetic flux, field strength, and field lines.

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Explores Maxwell's equations, Faraday's law, Ampère's law, and the prediction of nontrivial phenomena.

Maxwell's Equations: Derivation and Implications PHYS-114: General physics: electromagnetism

Explores the derivation and implications of the 4th Maxwell's equation, emphasizing the importance of charge conservation and the role of displacement current.

Maxwell's Equations: Practical Significance MICRO-313: Actuators and Electromagnetic systems I MOOC: Conversion electromécanique I

Illustrates the practical implications of Maxwell's equations through real-life demonstrations.

Maxwell's Equations and Displacement Current PHYS-201(d): General physics: electromagnetism

Explores Maxwell's equations, displacement current, and constituent equations in electromagnetism problem-solving.