Question

The electric field of an electromagnetic wave in free space is given by $E=10\cos ({10}^{7}t+kx)\hat{j}V/m$, where $t$ and $x$ are in seconds and metres respectively.
Find the wavelength of the electromagnetic wave.

• A. $152.23$ $m$
• B. $252.02$ $m$
• C. $178.4$ $m$
• D. $188.4$ $m$

Answer 1

The correct option is D $188.4$ $m$

As given,
$E=10\cos \left({10}^{7}t+kx\right)$
Comparing it with the standard equation of electromagnetic waves,
$E=E_0\cos \left(\omega t+kx\right)$
Here, $E_0$ = $10V/m$
$\omega ={10}^{7}rad/s$
$\therefore c=v\lambda =\frac{\omega \lambda }{2\pi }or\lambda =\frac{2\pi c}{\omega }=\frac{2\pi \times 3\times {10}^8}{{10}^7}=188.4m$