Question

What are electromagnetic waves? Draw their propagation diagram. Show the electric field amplitude and magnetic field amplitude in the propagation diagram.

Hint:

Electromagnetic waves are transverse waves of mutually perpendicular oscillating E and B fields; in the diagram show E along one axis (amplitude E0), B along the perpendicular axis (amplitude B0), both perpendicular to the propagation direction.

Answer 1

Step 1: Definition.
Electromagnetic waves are waves in which a changing electric field and a changing magnetic field are mutually perpendicular to each other and also perpendicular to the direction of propagation of the wave. They are produced by accelerating (oscillating) electric charges and do not need any material medium to travel; they can propagate through vacuum.

Step 2: Key properties.
They are transverse waves. In free space they travel with the speed of light
\[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3\times10^{8}\ \text{m/s} \]
The electric field \( \vec{E} \) and magnetic field \( \vec{B} \) oscillate in phase, and their magnitudes are related by \( c = E_0/B_0 \).

Step 3: Propagation diagram (described).
Take the wave travelling along the x-axis. The electric field \( \vec{E} \) oscillates as a sine curve in the x-y plane (up and down along the y-axis) with amplitude \( E_0 \). The magnetic field \( \vec{B} \) oscillates as a sine curve in the x-z plane (in and out along the z-axis) with amplitude \( B_0 \), in phase with \( \vec{E} \).

Described figure: two sine waves sharing the same x-axis; the E-wave lies in the vertical (x-y) plane with its peak marked \( E_0 \), and the B-wave lies in the horizontal (x-z) plane with its peak marked \( B_0 \). The three directions \( \vec{E} \), \( \vec{B} \), and the propagation direction form a right-handed set (\( \vec{E}\times\vec{B} \) points along the direction of travel).
\[\boxed{\vec{E}\perp\vec{B}\perp\text{direction of propagation};\ c=E_0/B_0}\]