Question

The electric field part of an electromagnetic wave in vacuum is
$E = 3.1 \frac{N}{C} cos \left[\left(1.8 \frac{rad}{m}\right) y + \left(5.4 \times 10^{8} \frac{rad}{s}\right)t\right] \hat{i}$
The wavelength of this part of electromagnetic wave is

• A. $1.5 \,m$
• B. $2 \,m$
• C. $2.5 \,m$
• D. $3.5 \,m$

Answer 1

Answer: (D)

Given $E = 3.1 \,N \,C ^{-1} \times$
$cos\left[\left(1.8\,rad\,m^{-1}\right)y +\left(5.4 \times 10^{8}\, rad \,s^{-1}\right)t\right] \hat{i}\quad ... \left(i\right)$
Comparing $\left(i\right)$ with the equation
$E = E_{0} \,cos \left(ky + \omega t\right)\quad...\left(ii\right)$
We get, $k = 1.8 \,rad\, m^{-1}$,
$E_{0} = 3.1\, N\, C^{-1}$,
$c = 3 \times 10^{3}m s^{-1}$,
$\omega = 5.4 \times 10^{8}\, rad \,s^{-1}$
Now, $\lambda = \frac{2\pi}{k}$
$ = \frac{2 \times 22}{1.8 \times 7} = 3.5\,m$