Question

The electric fixed intensity associated with a plane wave travelling in a perfect dielectric medium having μ = μ₀ is given by \(\vec E = 10\cos \left( {6\pi \times {{10}^7}t - 0.4\pi z} \right)\hat i\frac{V}{m}.\)

Find the phase velocity.

1. 1.5 × 10⁸ m/s
2. 3 × 10⁸ m/s
3. 0.75 × 10⁸ m/s
4. 6 × 10⁸ m/s

Answer 1

Correct Answer - Option 1 : 1.5 × 10⁸ m/s

Concept:

Let an electromagnetic wave is denoted by

\(E = {E_o}sin\;\left( {kz\;-\omega t} \right)\hat i\)

Wavelength: - \(\lambda = \frac{{2\pi }}{k}\), where k = wave number

Frequency \(f = \frac{\omega }{{2\pi \;}}\) where, ω is the angular frequency

speed of propagation: - speed of wave \(\left( v \right) = \lambda f = \frac{{2\pi }}{k} \times \frac{\omega }{{2\pi }}\; = \frac{\omega }{k}\) 

In vacuum, the speed of electromagnetic wave is equal to the speed of light c

Calculation:

Phase velocity or speed of propagation (v)

\(= \frac{w}{k} = \frac{{6\pi \times {{10}^7}}}{{0.4\pi }} = 1.5 \times {10^8}\;m/s\)