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Inequalities and Operators Involving Magnetic Fields

  • Alexander A. Balinsky
  • W. Desmond Evans
  • Roger T. Lewis
Chapter
Part of the Universitext book series (UTX)

Abstract

In classical mechanics the motion of charged particles depends only on electric and magnetic fields E, B which are uniquely described by Maxwell’s equations:
$$\displaystyle{\nabla \cdot \mathbf{E} = 4\pi \rho,}$$
$$\displaystyle{\nabla \cdot \mathbf{B} = 0,}$$
$$\displaystyle{\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t},}$$
$$\displaystyle{\nabla \times \mathbf{B} = 4\pi \mathbf{J} + \frac{\partial \mathbf{E}} {\partial t}.}$$

Keywords

Gauge Transformation Zero Mode Connected Domain Magnetic Potential Form Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alexander A. Balinsky
    • 1
  • W. Desmond Evans
    • 1
  • Roger T. Lewis
    • 2
  1. 1.School of MathematicsCardiff UniversityCardiffUK
  2. 2.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

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