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Explain the importance of Maxwell’s correction.

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#### Solution

- Ampere’s law says that only an electric current can produce a magnetic field. If Ampere’s law alone is true, there will not be any radiation.
- Maxwell’s correction term `(mu_0epsilon_0 ("d"phi_"E")/"dt")`
- In ampere’s law ensures that time-varying electric field or displacement current can also produce a magnetic field.
- Though conduction current is zero in an empty space displacement current does exist. So Maxwell equation becomes

`oint vec"B" * vec"dI" = mu_0epsilon_0 ("d"φ_"E")/"dt"` - Faraday’s law this time-varying magnetic field produces again time-varying electric field and so on.
- The coupled time-varying electric and magnetic fields travel through empty space with the speed of light and is called an electromagnetic wave.
- Even though Maxwell initially started with a purely symmetry argument his correction term explains one of the important aspects of the universe namely the existence of electro magnetic waves.

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