For an electromagnetic wave propagating in $+y$ direction the electric field is $\vec{E}=\frac{1}{\sqrt{2}} E_{y z}(x, t) \hat{z}$ and the magnetic field is $\vec{ B }=\frac{1}{\sqrt{2}} B _{ z }( x , t ) \hat{ y }$
For an electromagnetic wave propagating in $+y$ direction the electric field is $\vec{E}=\frac{1}{\sqrt{2}} E_{y z}(x, t) \hat{y}$ and he magnetic field is $\vec{ B }=\frac{1}{\sqrt{2}} B _{ yz }( x , t ) \hat{ z }$
For an electromagnetic wave propagating in $+ x$ direction the electric field is $\vec{ E }=\frac{1}{\sqrt{2}} E _{ yz }( y , z , t )(\hat{ y }+\hat{ z })$
and the magnetic field is $\vec{ B }=\frac{1}{\sqrt{2}} B _{ yz }( y , z , t )(\hat{ y }+\hat{ z })$
For an electromagnetic wave propagating in $+x$ direction the electric field is $\vec{E}=\frac{1}{\sqrt{2}} E_{y z}(x, t)(\hat{y}-\hat{z})$ and eh magnetic field is $B =\frac{1}{\sqrt{2}} B _{ yz }( x , t )(\hat{ y }+\hat{ z })$
Show Solution
The Correct Option isD
Solution and Explanation
To understand which statement is correct, we need to recall some fundamental properties of electromagnetic waves in a vacuum:
Direction of Propagation: In electromagnetic waves, the electric field \( \vec{E} \), magnetic field \( \vec{B} \), and the wave vector indicating the direction of propagation (\( \vec{k} \)) are mutually perpendicular. This means if the wave is propagating in the \( +x \) direction, the electric and magnetic fields are in the \( y \) and \( z \) directions.
Example: For a wave propagating in the \( +x \) direction, the \( \vec{E} \) field might be in the \( y \) direction and the \( \vec{B} \) field in the \( z \) direction, or vice versa, forming a right-handed coordinate system.
Now, let's analyze the given options:
Option 1 describes a wave propagating in the \( +y \) direction with both fields having components in the \( x \) and \( z \) directions. This configuration doesn't satisfy the mutual perpendicular requirement since the propagation is along \( y \).
Option 2 again concerns propagation in the \( +y \) direction with both fields described. However, the configurations of the fields are not correct for propagation along \( y \).
Option 3 involves propagation in the \( +x \) direction with both electric and magnetic fields having components in both \( y \) and \( z \). This option doesn't satisfy the perpendicular requirement correctly as both fields cannot simultaneously be in the same plane.
Option 4: For an electromagnetic wave propagating in the \( +x \) direction, it states:
Electric Field: \(\vec{E} = \frac{1}{\sqrt{2}} E_{yz}(x, t)(\hat{y} - \hat{z})\)
Magnetic Field: \(\vec{B} = \frac{1}{\sqrt{2}} B_{yz}(x, t)(\hat{y} + \hat{z})\)
This option correctly illustrates the components being perpendicular to the direction of wave propagation \( +x \). The sum and difference in the components for \( \hat{y} \) and \( \hat{z} \) show proper orthogonal behavior required for electromagnetic waves.
Based on the mutual perpendicularity requirement of \( \vec{E} \), \( \vec{B} \), and the direction of wave propagation, Option 4 is indeed the correct statement for an electromagnetic wave propagating in the \( +x \) direction.
