Electric field in a plane electromagnetic wave is given by E = 50 sin(500x - 10 × 10¹⁰ t) V/m The velocity of electromagnetic wave in this medium is :
(Given C = speed of light in vacuum)

Solution

Physics sir · 3 steps

Read ω and k straight off the sine, divide them, and compare with 3 × 10⁸.

1. Match the form. A plane wave has the form E = E₀ sin(kx - ω t). Matching terms gives k = 500 m⁻¹ and ω = 10 × 10¹⁰ = 10¹¹ rad s⁻¹.

   v = ω/k = 10¹¹/500 = 2 × 10⁸ m s⁻¹

2. Compare with C. v/C = (2 × 10⁸)/(3 × 10⁸) = 2/3. The wave is slower than in vacuum, as it should be in a material medium.
3. So. The speed of the wave in this medium is 2/3C, option (c).

The idea to keep. For any wave written as sin(kx - ω t), the speed is ω / k. The amplitude plays no part in it.

Answer from the NTA final answer key. Solution by PrepWiser.