Question

A plane electromagnetic wave propagating in the $x-direction$ has wavelength of $6.0\, mm$. The electric field is in the $y-direction$ and its maximum magnitude is $33\,Vm^{-1}$. The equation for the electric field as function of $x$ and $t$ is

• A. $ 11\,\sin \,\pi \left( t-x/c \right) $
• B. $ 33\,\sin \,\pi \times 10^{11}\left( t-x/c \right) $
• C. $ 33\,\sin \,\pi \left( t-x/c \right) $
• D. $ 11\,\sin \,\pi \times 10^{11}\left( t-x/c \right) $

Answer 1

Answer: (B)

Angular frequency,
$\omega =2 \pi v=\frac{2 \pi c}{\lambda}$
$=\frac{2 \pi \times 3 \times 10^{8}}{6 \times 10^{-3}} $
$=\pi \times 10^{11} rads ^{-1}$
The equation for the electric field, along $Y$-axis in the electromagnetic wave is
$E_{y} =E_{0} \sin \omega\left(t-\frac{x}{c}\right) $
$=33 \sin \pi \times 10^{11}(t-x / c)$