Question

The electric field part of an electromagnetic wave in a medium is represented by
$E_x=0,$
$E_y=\left(2.5\frac{\text{N}}{\text{C}}\right)\cos [(2\pi \times {10}^6\text{rad/s})t-(\pi \times {10}^{-2}\text{rad/m})x],$
$E_z=0$.
The wave is :

• A. Moving along $-x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $200\text{m}$.
• B. Moving along $+y$ direction with frequency $2\pi \times {10}^6\text{Hz}$ and wavelength $200\text{m}$.
• C. Moving along $+x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $100\text{m}$.
• D. Moving along $+x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $200\text{m}$.

Answer 1

The correct option is D Moving along $+x$ direction with frequency ${10}^6\text{Hz}$ and wavelength $200\text{m}$.

From given data,
$E_y=\left(2.5\frac{\text{N}}{\text{C}}\right)\cos [(2\pi \times {10}^6\text{rad/s})t-(\pi \times {10}^{-2}\text{rad/m})x]$
moves along direction $+x$ axis, having
wavelength $\lambda =\frac{2\pi }{k}=\frac{2\pi }{\pi \times {10}^{-2}}=200\text{m}$ and
Frequency $f=\frac{\omega }{2\pi }=\frac{2\pi \times {10}^6}{2\pi }={10}^6\text{Hz}$