The electric field amplitude of an electromagnetic wave is \( 100\,\mathrm{N\,C^{-1}} \) and its frequency is 50 MHz. What is the magnitude of wave vector \( (k) \). (given speed of electromagnetic wave is \( 3\times10^{8}\,\mathrm{m\,s^{-1}} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{\pi}{3} \)
The magnitude of the wave vector is \( k = \frac{2\pi}{\lambda} \), and the wavelength follows from the speed and frequency of the wave, \( \lambda = \frac{c}{\nu} \).
\( \displaystyle \lambda = \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{50\times10^{6}\,\mathrm{Hz}} = 6\,\mathrm{m} \)
\( \displaystyle k = \frac{2\pi}{6\,\mathrm{m}} = \frac{\pi}{3}\,\mathrm{rad\,m^{-1}} \)