Question

Derive an expression for the velocity of em waves in vacuum

Answer 1

The required velocity expression for a particle in vacuum. ID = εo dΦE  / dt

Explanation:

Solution:

Ampere Maxwell law states that the line integral of magnetic field along a closed loop around a current carrying wire is equal to μo times, the sum of current in the wire and the displacement current (ID).

Thus,

Φ  β.dl = μo( I + ID)

In absence of current in the wire.

Φ  β.dl = μo( ID)

Maxwell assumed as changing magnetic field produces electric field, changing electric field should also produce magnetic field.

By Gauss theorem we have.

Φ  E.ds = q /εo

=> q = εoΦ  E .ds

=> dq / dt = εo d / dt Φ  E .ds

ID = εo dΦE  / dt

This give the required velocity expression for a particle in vacuum.

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