Question

A plane electromagnetic wave propagating in the $x-direction$ has wavelength of $6.0mm$. The electric field is in the $y-direction$ and its maximum magnitude is $33V{m}^{-1}$. 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,
$\omega =2\pi v=\frac{2\pi c}{\lambda }$
$=\frac{2\pi \times 3\times 10^8}{6\times 10^{-3}}$
$=\pi \times 10^{11}rad{s}^{-1}$
The equation for the electric field, along $Y$-axis in the electromagnetic wave is
$E_y=E_0\sin \omega \left(t-\frac{x}{c}\right)$
$=33\sin \pi \times 10^{11}(t-x/c)$