Question

The electric field of an electromagnetic wave in free space is given by $\vec{E}=10\cos \left(10^{7}t+kx\right)\hat{j}V/m$, where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
(1) the wavelength $\lambda$ is $188.4m$.
(2) the wave number $k$ is $0.33rad/m$.
(3) the wave amplitude is $10V/m$.
(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)

Answer 1

Answer: (D)

As given
$E=10\cos \left(10^{7}t+kx\right)$
Comparing it with standard equation of e.m.
wave,
$E=E_0\cos (\omega t+kx)$
Amplitude $E_0=10V/m$
and $\omega =10^{7}rad/s$
$\because c=v\lambda =\frac{\omega \lambda }{2\pi }$
or $\lambda =\frac{2\pi c}{\omega }=\frac{2\pi \times 3\times 10^8}{10^7}=188.4m$
Also, $c=\frac{\omega }{k}$
or $k=\frac{\omega }{c}=\frac{10^7}{3\times 10^8}=0.033$
The wave is propagating along $y$ direction.