
Why is Maxwell’s modification of Ampère’s law essential to the existence of

Answer to Problem 1FTD
Explanation of Solution
According to Faraday’s law, the change in magnetic flux causes electric field. Faraday’s law is given as,
Here,
Ampere’s law is given as,
Here,
Since electricity and magnetism has a near symmetry, the change in electric flux can cause magnetism. Thus, the Ampere’s law should contain an extra term for change in magnetic flux. Amperes law without Maxwell’s modification can only applicable in steady current. Thus, for varying current, there should be a modification of Ampere’s equation without affecting the validity of Ampere’s law in steady case. The Amperes law with Maxwell’s modification is given as,
Here,
Since electromagnetic waves propagates by means of propagation of perpendicular electric and magnetic fields, the induction of the fields due to the flux change should be present. Thus, the modification of Ampere’s law is important for the existence of electromagnetic wave.
Conclusion:
Maxwell’s modification of Ampere’s law is essential to the existence of electromagnetic waves since the electromagnetic the generation of magnetic field component of the electromagnetic wave is the resultant of a change in electric flux.
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