What would have been the Maxwell's equations if there were magnetic monopoles?

In summary, the conversation discusses the concept of magnetic monopoles and their inclusion in Maxwell's equations. There is a disagreement about the validity of certain equations and whether they should include the concept of magnetic charge density. The idea of a charge in Maxwell's theory is also explored, with a differentiation between a point singularity and a discontinuity of polarization. Additionally, there is mention of other theories that allow for the creation and evaporation of magnetic monopoles.
  • #1
roshan2004
140
0
I am specifically talking about differential forms of Maxwell's equations here-
I think ( Tell me if I am incorrect here...) since the divergence of the magnetic field is zero, we have to say it is incorrect for my above problem, so the equation should have been the divergence of magnetic field is magnetic charge density divided by what ? ( Is it the permeability of free space ?)
Also, I think ( not too sure) the faraday's law: [itex]\frac{-\partial B}{\partial t}[/itex] is also incorerct here- but I am not sure why is it and what should have been the equation for the above condition ?
 
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  • #3
Heaviside's original rendition of the "Maxwell Equations" in vector form is expressed where a magnetic charge may be present. In his usage, he would normalize away the charge after the bulk of the calculations for any particular problem were done.

A charge, in Maxwell's theory is a more general concept than monopole, if by monopole you mean point singularity. A charge is a discontinuity of polarization and may therefore be a point, line segment, line or surface.

In Dirac theory and in related theories such as the Harmuth ansatz, the magnetic monopole or charge is not necessarily a persistent object. It can be created and evaporated in a very short period of time under certain conditions.
 

1. What are Maxwell's equations?

Maxwell's equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields. They were developed by physicist James Clerk Maxwell in the 19th century and are a cornerstone of classical electromagnetism.

2. What are magnetic monopoles?

Magnetic monopoles are hypothetical particles that possess only one magnetic pole, either north or south, instead of the usual dipole configuration of magnets. They have never been observed in nature, but their existence is predicted by certain theories, including some versions of string theory.

3. What would have been the Maxwell's equations if there were magnetic monopoles?

If magnetic monopoles existed, Maxwell's equations would have an additional term on the right-hand side known as the "magnetic charge density." This term would describe the behavior of magnetic monopoles and their interactions with electric and magnetic fields.

4. How would the presence of magnetic monopoles change our understanding of electromagnetism?

The existence of magnetic monopoles would significantly alter our understanding of electromagnetism. It would mean that electric and magnetic fields are not symmetric, as currently believed, and that there is a fundamental difference between electric and magnetic charges. It would also have implications for theories such as quantum electrodynamics.

5. Are there any real-world applications for the study of magnetic monopoles?

Although magnetic monopoles have not been observed, their study has potential applications in fields such as particle physics and cosmology. If magnetic monopoles do exist, they could provide insights into the fundamental nature of the universe and the origins of the universe's magnetic fields. Additionally, the search for magnetic monopoles has led to advancements in technologies such as particle accelerators and magnetic resonance imaging (MRI).

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