Question

The electric field of an electromagnetic wave in free space is given by
$\overrightarrow{E}=10cos({10}^{7}t+kx)\hat{j}V/m$, where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
(i) the wavelength $\lambda$ is $188.4m$.
(ii) the wave number $k$ is $0.33rad/m$.
(iii) the wave amplitude is $10V/m$.
(iv) the wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct?

• A. (c) and (d)
• B. (a) and (b)
• C. (b) and (c)
• D. (a) and (c)

Answer 1

The correct option is D (a) and (c)

As given:
$E=$ $10cos({10}^{7}t+kx)$
Comparing it with standard equation of e.m. wave,
$E=$ $E_{0}cos(\omega t+kx)$

Amplitude, $E_0=10$ $V/m$

and $\omega ={10}^7$ $rad/s$
$\because c=v\lambda =\frac{\omega \lambda }{2\pi }$ or $\lambda =\frac{2\pi c}{\omega }=\frac{2\pi \times 3\times {10}^8}{{10}^7}=188.4m$
Also,
$c=$ $\frac{\omega }{k}$ or $k=$ $\frac{\omega }{c}=\frac{{10}^7}{3\times {10}^8}$ = $0.033$

The wave is propagating along $y$ direction.