Q. The electric field of an electromagnetic wave in free space is given by $\overrightarrow{E} = 10\cos{\left( 10^{7}t + kx \right)\widehat{j}\ V/m}$, where $t$ and $x$ are in seconds and metres respectively. It can be inferred that (1) The wavelength $\lambda$ is $188.4\ m$ (2) The wave number $k$ is $0.33\ rad/m$ (3) The wave amplitude is 10 V/m (4) The wave is propagating along $+ x$ direction Which one of the following pairs of statements is correct
A) (3) and (4)
B) (1) and (2)
C) (2) and (3)
D) (1) and (3)
Explanation
(d) Amplitude $= 10\frac{V}{m}$
$C = \frac{\omega}{k}$
$3 \times 10^{8} = \frac{10^{7}}{k}$
$k = \frac{1}{30}$
$\frac{2\pi}{\lambda} = \frac{1}{30} \Rightarrow \lambda = 188.4m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.