Question

What are electromagnetic waves? Explain two characteristics of these waves.

Hint:

Electromagnetic waves are mutually perpendicular oscillating E and B fields that regenerate each other; note they are transverse, need no medium, and travel at c = 1/sqrt(mu0 epsilon0) = 3e8 m/s.

Answer 1

Step 1: Definition.
The waves in which mutually perpendicular electric and magnetic fields oscillate and which travel through space are called electromagnetic waves. A changing electric field produces a magnetic field and a changing magnetic field produces an electric field; these two fields continuously regenerate each other, and the disturbance propagates as a wave. Light, radio waves, X-rays and gamma rays are all electromagnetic waves.

Step 2: The fields and direction of travel.
In an electromagnetic wave the electric field \( \vec{E} \), the magnetic field \( \vec{B} \) and the direction of propagation are mutually perpendicular; the wave is therefore transverse.

Step 3: First characteristic.
• They are transverse and need no material medium. The oscillations of \( \vec{E} \) and \( \vec{B} \) are perpendicular to the direction of travel, and because the fields sustain each other the waves can travel through vacuum (empty space). This is why sunlight reaches us across empty space.

Step 4: Second characteristic.
• They travel with the speed of light in vacuum. All electromagnetic waves move through vacuum with the same speed
\[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3\times10^{8}\ \text{m/s} \]
where \( \mu_0 \) and \( \varepsilon_0 \) are the permeability and permittivity of free space. Also, the ratio of the field magnitudes is \( E/B = c \).

Step 5: Additional note.
Electromagnetic waves carry energy and momentum and are not deflected by electric or magnetic fields since they are uncharged.
\[\boxed{\text{Transverse } \vec{E}\perp\vec{B}\perp \text{travel; speed } c = 1/\sqrt{\mu_0\varepsilon_0} = 3\times10^8\ \text{m/s}}\]