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Question: The following Maxwell Equations govern electricity...

The following Maxwell Equations govern electricity and magnetisim.

Now imagine if instead of the above equations, the following equations instead governs magnetisum and electricty.

(Note: the only difference lies in the fourth equations where instead of partial of E, it is now partial of B.)

Now the important question is, if those 4 equations above govern electricty and magnetisum, would there still be electric magnetic waves in this world?

If so, with detail derive the equation to describe electric magnetic wave.

Expert Answer

Explanation / Answer

The fourth equation in Maxwell equations explain these two fact:

1. A flowing electric current (J) gives rise to a Magnetic Field that circles the current

2. A time-changing Electric Flux Density gives rise to a Magnetic Field that circles the E field.

Now you change in your fourth equation the electric flux density by magnetic flux density. And it is clear that the changing magnetic flux density can creat an emf or current by Faraday law of induction. Also there is no proof of equation you are imagine.

The original maxwell equations will not explain the presense of electromagnetic wave in nature. But using exact maxwell equations we only understand the nature of electromagnetic wave. These equations describe how electric and magnetic fields propagate, interact, and how they are influenced by objects.

For example the second equation, div(B)=0 will tell us the monopole in a magnet can never be exist. there will always be South pole with North pole and vice versa.

Conclusion:The existance of electromagnetic wave in nature can not verify by Maxwell equation.

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