On the Use of Auxiliary Vector Potentials as a Common Tool for Studying Electromagnetic Problems at Undergraduate Level

2003 ◽  
Vol 40 (2) ◽  
pp. 123-129
Author(s):  
Miguel A. Solano ◽  
ÁAngel Vegas ◽  
ÁAlvaro Gómez
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
The Other ◽  
Undergraduate Level ◽  
Electromagnetic Problems ◽  
Vector Potentials ◽  
Large Groups

Applications of Maxwell's equations to electromagnetic problems can be divided into two large groups: one dealing with radiation and scattering and the other with propagation. In this paper it is shown how both kinds of problem can be managed by means of the auxiliary vector potentials [Formula: see text] and [Formula: see text].

A Symmetric Formulation of Maxwell's Equations

1997 ◽  
Vol 12 (28) ◽  
pp. 2089-2101 ◽  
Author(s):  
Héctor A. Múnera ◽  
Octavio Guzmán
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
The Other ◽  
Independent Condition ◽  
Physical Problems ◽  
Symmetric Formulation ◽  
Current Densities ◽  
Symmetric Set ◽  
Scalar Potentials

The electromagnetic field formed by the pair (E, B) obeying Maxwell's equations (MEs) is reformulated as another pair (P, N) obeying a symmetric set of four equations tautologically equivalent to MEs. The symmetric set is formed by a pair of induction and a pair of source equations, each pair with exactly the same structure. In contrast to (E, B), charge and current densities contribute equally to both P and N. The equation of continuity is not an independent condition, but it is automatically fulfilled by any four-tuple (P, N, J, ρ) solving the symmetric MEs. The symmetric equations in terms of potentials may be explicitly solved for a variety of constraint conditions, thus leading to different classes of solutions. Each class represents a family of problems defined by the constraints. One such family is the conventional class of solutions of MEs. Some unexpected results regarding the conventional solutions of MEs in terms of potentials are: (a) it is a particular case, (b) it may contain magnetic scalar potentials, and (c) there is no Coulomb gauge, thus removing the magnetic transversality constraint. It is not known whether the other classes of solutions correspond to physical problems.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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