Question

What are electromagnetic waves ? By drawing its propagation diagram, show the electric field and magnetic field in it.

Hint:

When drawing the propagation diagram, ensure that the electric and magnetic fields are shown in phase, meaning they reach their maximum and zero values at the same points along the propagation axis.

Answer 1

Step 1: Definition of Electromagnetic Waves:
Electromagnetic (EM) waves are disturbances consisting of time-varying, sinusoidal electric and magnetic fields that oscillate perpendicular to each other and also perpendicular to the direction of wave propagation. Key properties include:
They are transverse in nature.
They are produced by accelerating electric charges.
They do not require a material medium for their propagation and can travel through a vacuum.
In a vacuum, they travel at a constant speed, the speed of light, \( c \approx 3 \times 10^8 \) m/s.
The electric field (\(\vec{E}\)) and magnetic field (\(\vec{B}\)) are always in the same phase.
Step 2: Propagation Diagram:
The diagram below shows the orientation of the electric field, magnetic field, and the direction of propagation for a plane-polarized electromagnetic wave. \begin{center} \begin{tikzpicture}[scale=1.5, transform shape] % Axes \draw[→, thick] (0,0,0) -- (4,0,0) node[below] {X (Propagation)}; \draw[→, thick] (0,0,0) -- (0,1.5,0) node[left] {Y (E-field)}; \draw[→, thick] (0,0,0) -- (0,0,1.5) node[below right] {Z (B-field)}; % E-field wave (in XY plane) \draw[red, thick] plot[domain=0:3.5, samples=100] (\x, {sin(\x*180/pi r)}, 0); % Arrows for E-field \foreach \x in {0.5, 2.5} { \draw[→, red, thick] (\x*pi/2, 0, 0) -- (\x*pi/2, {sin(\x*pi/2*180/pi r)}, 0) node[left] {\(\vec{E}\)}; } % B-field wave (in XZ plane) \draw[blue, thick] plot[domain=0:3.5, samples=100] (\x, 0, {sin(\x*180/pi r)}); % Arrows for B-field \foreach \x in {0.5, 2.5} { \draw[→, blue, thick] (\x*pi/2, 0, 0) -- (\x*pi/2, 0, {sin(\x*pi/2*180/pi r)}) node[below right] {\(\vec{B}\)}; } \end{tikzpicture} \end{center} Diagram Explanation:
The wave is propagating along the positive X-axis.
The electric field vector \(\vec{E}\) (in red) oscillates along the Y-axis.
The magnetic field vector \(\vec{B}\) (in blue) oscillates along the Z-axis.
At every point and every instant, \(\vec{E}\) is perpendicular to \(\vec{B}\), and both are perpendicular to the direction of propagation.
The vectors \(\vec{E}\), \(\vec{B}\), and the propagation vector \(\vec{k}\) form a right-handed system (\(\vec{E} \times \vec{B}\) points in the direction of propagation).