Lecture

Magnetic Field and Vector Potential: Relation with Current, Galvanometer, and Maxwell's Equations

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In course

PHYS-201(d): General physics : electromagnetism

The topics covered by the course are concepts of electromagnetism, properties of waves, and fluid mechanics. ...

Description

This lecture explores the relationship between the magnetic field and the vector potential, discussing the analogy between dipole moments in electrostatics and magnetism. The instructor explains the concept of a galvanometer for measuring current strength and polarity. The lecture delves into the construction of the vector potential function for the magnetic field, emphasizing its usefulness in certain scenarios. The instructor demonstrates how the vector potential can be used to derive Maxwell's equations in magnetostatics, highlighting the connection between the current density and the magnetic field. The lecture concludes with a summary of Chapter 4, emphasizing the interplay between current, vector potential, and magnetic field in electromagnetic theory.

Instructor

Dirk Grundler

Official source

Ontological neighbourhood

Physics

Electromagnetism: Electrodynamics

Related concepts (27)

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.

Current density

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Assume that A (SI unit: m2) is a small surface centred at a given point M and orthogonal to the motion of the charges at M.

Electromagnetism

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena.

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below.

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