Alternate expression for Maxwell's Equations

In summary, the conversation is about a person preparing for a course and struggling with deriving equations for E and H fields in terms of a magnetic current source. They are unsure about what a magnetic current source is and are seeking help from others or textbook resources.
  • #1
jimhalpert
1
0
Hello,

I'm prepping for a course I'm about to take and on the pre-course syllabus it said I should be able to:

"Derive the equations for E and H fields in terms of magnetic current source M."

It's been a long time since I've had an EM course, so I'm naturally lost. How would I go about doing this?
 
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  • #2
I don't know what a "magnetic current source" might be. If it's simply magnetization, the Ampere-Maxwell Law reads (in Heaviside-Lorentz units)

[tex]\vec{\nabla} \times \vec{H} - \frac{1}{c} \frac{\partial \vec{D}}{\partial t} = \vec{j} + \vec{\nabla} \times \vec{M}.[/tex]

If you have a model with magnetic monopoles, have a look in the usual standard textbooks like Jackson or Schwinger.
 

1. What are Maxwell's Equations?

Maxwell's Equations are a set of four partial differential equations that describe the behavior of electric and magnetic fields. They were developed by James Clerk Maxwell in the 19th century and are fundamental to our understanding of electromagnetism.

2. Why is there a need for an alternate expression of Maxwell's Equations?

The traditional form of Maxwell's Equations can be difficult to work with in certain situations, such as when dealing with non-Cartesian coordinate systems or in higher dimensions. An alternate expression can simplify the equations and make them more applicable to different scenarios.

3. What is the main difference between the traditional and alternate expressions of Maxwell's Equations?

The main difference is in the mathematical notation used. The traditional form uses vector calculus and the alternate form uses differential forms. This leads to different ways of representing the equations and performing calculations.

4. Are the alternate expressions of Maxwell's Equations equivalent to the traditional form?

Yes, the alternate expressions are mathematically equivalent to the traditional form. This means that they describe the same physical phenomena and can be used interchangeably. However, the alternate form may be more useful in certain situations.

5. How are the alternate expressions of Maxwell's Equations used in practical applications?

The alternate expressions are often used in theoretical physics and advanced engineering applications. They can also be used in numerical simulations and modeling, as well as in the development of new theories and concepts in electromagnetism.

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