Question

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

$E=3.1\cos [\left(1.8\frac{rad}{m}\right)y+(5.4\times {10}^8\frac{rad}{s})t]\hat{i}$...........(i)

Standard equation at electromagnetic wave in terms of electric field,

$E=E_0\cos (ky+wt)$.........(ii)

If the wave is moving in $-y$ direction

Wave length, $\lambda =\frac{2\pi }{Coefficientofy}$

$=\frac{2\pi }{1.8}=\frac{2\times 22/7}{1.8}$

$\lambda =\frac{44}{1.8\times 7}=3.49=3.5m$

Option - $D$