Newbie Problems on Electrodynamics

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SUMMARY

The discussion focuses on deriving the "magnetic field energy density" in a medium, represented by the equation \(\frac{1}{2}H \cdot B\). Participants emphasize the importance of understanding the conservation of energy equation in a medium, expressed as \(\nabla\cdot S + \frac{\partial v}{\partial t} = -E \cdot J\), where \(v = \frac{1}{2}(E \cdot D + B \cdot H)\). It is clarified that this derivation is applicable primarily to linear quasistatic media, where \(D\) is proportional to \(E\) and \(H\) is proportional to \(B\). The discussion highlights the nuances of working with non-linear media.

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  • Understanding of Maxwell's equations
  • Familiarity with electromagnetic field theory
  • Knowledge of Poynting vector and energy density concepts
  • Basic calculus for derivation processes
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  • Study the derivation of magnetic field energy density in various media
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Students and professionals in physics, particularly those specializing in electromagnetism, electrical engineers, and researchers working with electromagnetic fields in various media.

Wong
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May anyone please show me how to derive the "magnetic field energy density" in a medium, which equals [tex]\frac{1}{2}H \cdot B[/tex]?

I would be very pleased if anyone could show me how to derive (step-bystep) the conservation of energy equation *in a medium* (not in vacuum) i.e. [tex]\nabla\cdot S + \frac{\partial v}{\partial t} = -E \cdot J[/tex], where [tex]v = \frac{1}{2}(E \cdot D + B \cdot H)[/tex] and S is the poynting vector. (N.B. The medium may not be linear i.e. D may not be proportional to E, H not to B)
 
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Sorry for asking...I understand now, that the equation I posted only works for linear quasistatic media. Thus D should be proportaional to E and H to B and the derivation is essentially the same as in the vacuum case.
 

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