Question 212: EM waves

Question

The electric field of an electromagnetic wave in free space is given by $$\overrightarrow E  = 10\cos ({10^7}t + kx)\widehat j\,\,V/m,$$ 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 ?

Accepted Answer

As given, $$E  = 10\cos ({10^7}t + kx)\widehat j\,\,V/m$$
here amplitude E
0
= 10 V/m and $$\omega $$ = 10
7
rad/s
As c = $$
u \lambda  = {{\omega \lambda } \over {2\pi }}$$
$$ \Rightarrow $$ $$\lambda $$ = $${{2\pi c} \over \omega }$$ = $${{2\pi  	imes 3 	imes {{10}^8}} \over {{{10}^7}}}$$ = 188.4 m
Also, c = $${\omega  \over k}$$
$$ \Rightarrow $$ k = $${\omega  \over c} = {{{{10}^7}} \over {3 	imes {{10}^8}}}$$ = 0.033
The wave is propagating along y direction.

Answer

(3)  and  (4)

Answer

(1)  and  (2)

Answer

(2)  and  (3)

Answer

(1)  and  (3)

EM waves

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