Question

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

Answer 1

Answer: (D)

As given
$E=10 \cos \left(10^{7} t+k x\right)$
Comparing it with standard equation of e.m.
wave,
$E=E_{0} \cos (\omega t+k x)$
Amplitude $E_{0}=10 V / m$
and $\omega=10^{7} \,rad / s$
$\because c=v \lambda=\frac{\omega \lambda}{2 \pi}$
or $\lambda=\frac{2 \pi c}{\omega}=\frac{2 \pi \times 3 \times 10^{8}}{10^{7}}=188.4\, m$
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.