Question

Choose the correct answer from the alternatives given.
The electric field part of an electromagnetic wave in vacuum is
$E=3.1\frac{N}{C}cos\left[\left(1.8\frac{rad}{m}\right)\right]y+(5.4\times {10}^8\frac{rad}{8})t]\stackrel{\wedge }{i}$
The wavelength of this part of electromagnetic wave is

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

Answer 1

The correct option is D $3.5m$

Given: The electric field of the wave is $E=3.1N{C}^{-1}\times \cos \left[\right(1.8rad{m}^{-1})y+(5.4\times {10}^{8}rad{s}^{-1}\left)t\right]\hat{i}$
To find: The wavelength of the electromagnetic wave.

The standard equation for the electric field is:

$E=E_{0}cos(ky+\omega t)$ .........(i)

On comparing the equation of field with standard equation, We get,

$k=1.8rad{m}^{-1},$
We know that,

$k=\frac{2\pi }{\lambda }$
So,

$\lambda =\frac{2\pi }{k}\Rightarrow \frac{2\times \pi }{1.8}=3.5m$

So, option $\left(D\right)$ is correct.