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Electromagnetic Fields
Published in Christos Christopoulos, Principles and Techniques of Electromagnetic Compatibility, 2022
The magnetic field components are obtained from the curl of the vector potential and are H¯ϕ=jω[p¯z] sin θ4π(1r2+jβr)H¯r=H¯θ=0
All About Wave Equations
Published in Bahman Zohuri, Patrick J. McDaniel, Electrical Brain Stimulation for the Treatment of Neurological Disorders, 2019
Bahman Zohuri, Patrick J. McDaniel
Also note that the gauge transformation given by Eqs. (2.285a) and (2.285b) does not allow a gauged expression of Δδ* to be formed such that both gauge and the vector potential terms will simultaneously cancel. Thus, setting a gauge such that the vector potential is reduced to zero, i.e., A→′=A→−(ℏc/q)∇x=0, the gauge pseudo-potentials remain, thereby assuring that the phase difference does not change upon a gauge transformation. This result holds whether the vector potential has curl or is curl-free.
The static and quasistatic electromagnetic fields
Published in Edward J. Rothwell, Michael J. Cloud, Electromagnetics, 2018
Edward J. Rothwell, Michael J. Cloud
[Magnetic field of uniformly magnetized ball by curl of vector potential] Consider a ball of radius a, residing in free space and having permanent magnetization M(r)=M0z^ $ \mathbf{M}(\mathbf{r})= M_0 \hat{\mathbf{z}} $ . Find the magnetic field by computing the curl of the vector potential.
Modeling the Interaction of Electrodynamic Fields to Circuit Elements
Published in IETE Journal of Education, 2018
Electrodynamics literature uses the term gauge to define the relationship between sources (charge densities ρ and current densities ) and the resulting potential fields (electric potential Φ and magnetic vector potential ). The divergence of the magnetic vector potential ( i.e.) establishes the gauge. Students are most familiar with the Coulomb gauge () from magnetostatic course material. However, students may not be exposed to the infinite number of gauge possibilities (refer to Section A.5 in Appendix 1 for further information on gauges).
The mode generation due to the wave transmission phenomena from a loss free isotropic cylindrical metallic waveguide to the semi-bounded plasma waveguide
Published in Waves in Random and Complex Media, 2021
Samaneh Najari, Bahram Jazi, Sajad Jahanbakht
The Maxwell’s equations consist of a set of coupled first-order partial differential equations relating to the components of the electric and the magnetic fields. One of these equations is: Therefore, the magnetic field in terms of a vector potential can be defined