Symmetry Arguments and the Infinite Wire with a Current

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Thread starter Orodruin
Start date May 17, 2022
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SUMMARY

This discussion centers on the application of symmetry arguments to analyze the magnetic field around an infinite wire carrying a constant current, denoted as ##I##. It emphasizes that, similar to Gauss's law for electric fields, the magnetic field, represented by the vector ##\vec B##, cannot possess components in the radial direction or along the wire itself. The conversation highlights the importance of understanding the transformation properties of vectors, particularly under rotations and reflections, to support these conclusions.

PREREQUISITES

Understanding of Gauss's law for electric fields
Familiarity with magnetic field concepts and vector representation
Knowledge of symmetry arguments in physics
Basic principles of spatial transformations in vector fields

NEXT STEPS

Study the transformation properties of magnetic fields under spatial transformations
Explore advanced applications of Gauss's law in electromagnetism
Investigate the implications of symmetry arguments in other physical systems
Learn about the mathematical representation of vector fields in electromagnetism

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Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of magnetic fields and symmetry arguments in theoretical physics.

May 17, 2022

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Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric charge distribution or around an infinite wire carrying a charge per unit length are standard examples. This Insight explores similar arguments for the magnetic field around an infinite wire carrying a constant current ##I##, which may not be as familiar. In particular, our focus is on the arguments that can be used to conclude that the magnetic field cannot have a component in the radial direction or in the direction of the wire itself.
Transformation properties of vectors
To use symmetry arguments we first need to establish how the magnetic field transforms under different spatial transformations. How it transforms under rotations and reflections will be of particular interest. The magnetic field is described by a vector ##\vec B## with both...

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