Electromagnetic field

In the physics of electromagnetism, an electromagnetic field is a field composed of two related vector fields: the electric field and the magnetic field. When referred to as the electromagnetic field, the field is imagined to encompass all of space; typically an electromagnetic field is considered to be limited to a local area around an object in space.

The electromagnetic field as a feedback loop

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

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The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:

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• charges generate fields
• Gauss's law Coulomb's law: charges generate electric fields
• Ampère's law: currents generate magnetic fields ($star$)
• the fields interact with each other
• displacement current: changing electric field acts like a current, generating vortex of magnetic field
• Faraday induction: changing magnetic field induces (negative) vortex of electric field
• Lenz's law: negative feedback loop between electric and magnetic fields
• Maxwell-Hertz equations: simplified version of Maxwell's equations
• electromagnetic wave equation
• fields act upon charges
• Lorentz force: force due to electromagnetic field
• electric force: same direction as electric field
• magnetic force: perpendicular both to magnetic field and to velocity of charge ($star$)
• charges move
• continuity equation: current is movement of charges

Phenomena in the list are marked with a star (star) if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz transformations to electric fields and static charges. This means that the magnetic field ends up being (conceptually) reduced to an appendage of the electric field, i.e. something which interacts with reality only indirectly through the electric field.

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