Question 23: EM waves

Question

An electromagnetic wave travelling in the x-direction has frequency of 23 $$ 	imes $$ 10
14
Hz and electric field amplitude of 27 Vm
$$-$$1
. From the options given below, which one describes the magnetic field for this wave ?

Accepted Answer

We know that
$$
\begin{gathered}
E_o=c B_o \Rightarrow B_o=\frac{E_o}{c}=\frac{27}{3 	imes 10^8}=9 	imes 10^{-8}(\mathrm{~T}) \\
\omega=2 \pi f=2 \pi 	imes 2 	imes 10^{14} \mathrm{rad} / \mathrm{s} ; \\
K=\frac{2 \pi}{\lambda}=\frac{2 \pi f}{C}=2 \pi 	imes \frac{2 	imes 10^{14}}{3 	imes 10^8}=2 \pi 	imes\left(0.67 	imes 10^{-6}ight) / \mathrm{m}
\end{gathered}
$$
Since $\vec{B} \perp$ wave direction (x-axis)
$$
\begin{aligned}
B & =B_o \sin (K x-\omega t)=B_o \sin 2 \pi\left(\frac{x}{\lambda}-f tight) \\
& =9 	imes 10^{-8} \sin 2 \pi\left(\frac{x}{1.5 	imes 10^6}-2 	imes 10^{14} tight)
\end{aligned}
$$

Answer

$$\overrightarrow B $$ (x, t) = (3 $$ 	imes $$ 10
$$-$$8
T) $$\widehat j$$
sin [ 2$$\pi $$ (1.5 $$ 	imes $$ 10
$$-$$8
x $$-$$ 2 $$ 	imes $$ 10
14
t)]

Answer

$$\overrightarrow B $$ (x, t) = (9 $$ 	imes $$ 10
$$-$$8
T) $$\widehat k$$
sin [ 2$$\pi $$ (1.5 $$ 	imes $$ 10
$$-$$6
x $$-$$ 2 $$ 	imes $$ 10
14
t)]

Answer

$$\overrightarrow B $$ (x, t) = (9 $$ 	imes $$ 10
$$-$$8
T) $$\widehat i$$
sin [ 2$$\pi $$ (1.5 $$ 	imes $$ 10
$$-$$8
x $$-$$ 2 $$ 	imes $$ 10
14
t)]

Answer

$$\overrightarrow B $$ (x, t) = (9 $$ 	imes $$ 10
$$-$$8
T) $$\widehat j$$
sin [(1.5 $$ 	imes $$ 10
$$-$$6
x $$-$$ 2 $$ 	imes $$ 10
14
t)]

EM waves

An electromagnetic wave travelling in the x-direction has frequency of 23 $ \times 10 14 Hz and electric field amplitude of 27 Vm -$1 . From the options given below, which one describes the magnetic field for this wave ?

Choose the correct answer: