Question

An electromagnetic wave is propagating in vacuum along $z-$axis. The electric field component is given by $E_x=E_{\circ }\sin (kz-\omega t)$, then the magnetic component is,

• A. $B_x=\frac{E_{\circ }}{C}\sin (kz-\omega t)$
• B. $B_y=\frac{B_{\circ }}{C}\sin (kz-\omega t)$
• C. $B_y=\frac{E_{\circ }}{C}\sin (kz-\omega t)$
• D. $B_y=B_{\circ }C\sin (kz-\omega t)$

Answer 1

The correct option is C $B_y=\frac{E_{\circ }}{C}\sin (kz-\omega t)$

Given:
$E_x=E_{\circ }\sin (kz-\omega t)$

From the equation of the electromagnetic wave, we can say that the wave is travelling along the $+z-$ axis and electric field is pointed along the $x-$axis.

We know that the direction of propagation of electromagnetic wave is given by,
$\hat{v}=\hat{E}\times \hat{B}$

Where $\hat{E}$ is the direction of electric field and $\hat{B}$ is the direction of magnetic field.

Here, $\hat{v}=\hat{k},\hat{E}=\hat{i}\Rightarrow \hat{B}=\hat{j}$

Hence magnetic filed lies along the $y-$axis.

Also, amplitude of magnetic filed is given by,
$B_{\circ }=\frac{E_{\circ }}{C}(\because c=\frac{E_o}{B_o})$

Therefore, the equation of magnetic filed is given by,
$B_y=\frac{E_{\circ }}{C}\sin (kz-\omega t)$

Hence, $\left(C\right)$ is the correct answer.

Why this question : This question tests your basic understanding of the equation of the electromagnetic wave.