Question

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

• A. For an electromagnetic wave propagating in +y direction the 1 A electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)\hat{z}$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{B}_z(x,t)\hat{y}$
• B. For an electromagnetic wave propagating in +y direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)\hat{y}$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{B}_z(x,t)\hat{z}$
• C. For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(y,z,t)(\hat{y}+\hat{z})$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{E}_{yz}(y,z,t)(\hat{y}+\hat{z})$
• D. For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}-\hat{z})$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}+\hat{z})$

Answer 1

Answer: (D)

For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}-\hat{z})$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}+\hat{z})$

Electromagnetic waves travel in the direction perpendicular to electric as well as magnetic field. Cross product of electric and magnetic field should give the direction of electromagnetic wave.

$\overrightarrow{E}\times \overrightarrow{B}$ = $\frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}-\hat{z})$$\times \frac{1}{\sqrt{2}}{E}_{yz}(x,t)(\hat{y}+\hat{z})$ = $E_{yz}^2(x,t)$ $\hat{x}$