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(a) Derive a relation for the velocity o...

(a) Derive a relation for the velocity of electromagnetic wave.
(b) An electromagnetic wave is travelling along Z-axis is described by magnetic field
`B_x =4 xx 10^(-10) sin ( omega t - kx -kz)T`
Find the maximum electric and magnetic field on an alpha particle moving along Y-axis with a speed of `5 xx 10^6` m/s. Charge on the electron is` 1.6 xx 10^(-19)` C.

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### Step-by-Step Solution **(a) Deriving the relation for the velocity of electromagnetic waves:** 1. **Understanding the Electromagnetic Wave:** An electromagnetic wave consists of electric (E) and magnetic (B) fields oscillating perpendicular to each other and also perpendicular to the direction of wave propagation. The general equations for the electric and magnetic fields can be represented as: \[ E(z, t) = E_{\text{max}} \cos(kz - \omega t) ...
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