Question 128: EM waves

Question

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in
free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable
magnetic field component in the electromagnetic wave ?

Accepted Answer

Since the wave is propagating in positive z-direction
So acceptable magnetic field component will be
$$\overrightarrow B  = {B_0}\sin \left( {kz - \omega t} ight)$$$$\widehat i$$
$$ \because $$ C = $${{{E_o}} \over {{B_o}}}$$
$$ \Rightarrow $$ $${B_o} = {{{E_o}} \over C}$$ = $${{60} \over {3 	imes {{10}^8}}}$$ = 2 $$ 	imes $$ 10
-7
and $$\omega  = 2\pi f$$ = 2$$\pi $$$$ 	imes $$23.9$$ 	imes $$10
9
= 1.5 ÃÂ 10
11
Hz
and k = $${\omega  \over c}$$ = $${{1.5 	imes {{10}^{11}}} \over {3 	imes {{10}^8}}}$$ = 0.5 ÃÂ 10
3
Note :
When wave is propagating in positive z-direction then sign of kz and $${\omega t}$$ should be opposite.
From option you can see only option D can be correct.

Answer

$$\overrightarrow B $$ = 2 × 10–7
 sin(1.5 × 102
x + 0.5 × 1011t) $$\widehat j$$

Answer

$$\overrightarrow B $$ = 60
 sin(0.5 × 103x + 0.5 × 1011t) $$\widehat k$$

Answer

$$\overrightarrow B $$ = 2 × 10–7
 sin(0.5 × 103
z + 1.5 × 1011t) $$\widehat i$$

Answer

$$\overrightarrow B $$ = 2 × 10–7
 sin(0.5 × 103
z - 1.5 × 1011t) $$\widehat i$$

EM waves

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

Choose the correct answer: