Question

What are electromagnetic waves? An electromagnetic wave is moving in the X direction and the directions of its electric and magnetic fields are Y and Z respectively. Write the general equations for the electric and magnetic fields of the wave. How are electromagnetic waves different from sound waves?

Hint:

EM waves are transverse oscillations of mutually perpendicular \( \vec{E} \) and \( \vec{B} \) that need no medium. With motion along X, write \( E_y = E_0\sin(kx-\omega t) \) and \( B_z = B_0\sin(kx-\omega t) \).

Answer 1

Step 1: What electromagnetic waves are.
Electromagnetic (EM) waves are waves in which an oscillating electric field and an oscillating magnetic field travel together through space. The two fields are mutually perpendicular and are also perpendicular to the direction of propagation, so EM waves are transverse. They are produced by accelerating (or oscillating) charges, require no material medium, and travel through vacuum with speed \( c = 3 \times 10^8 \) m/s.

Step 2: Set up the directions.
The wave travels along the \( +X \) axis. The electric field oscillates along \( Y \) and the magnetic field along \( Z \). This is consistent because \( \hat{Y} \times \hat{Z} = \hat{X} \), i.e. \( \vec{E} \times \vec{B} \) points along the direction of propagation.

Step 3: General field equations.
\[ E_y = E_0 \sin(kx - \omega t) \]
\[ B_z = B_0 \sin(kx - \omega t) \]
where \( k = \dfrac{2\pi}{\lambda} \) is the wave number, \( \omega = 2\pi\nu \) is the angular frequency, and the amplitudes satisfy \( \dfrac{E_0}{B_0} = c \).

Step 4: How EM waves differ from sound waves.
1. EM waves are transverse; sound waves are longitudinal.
2. EM waves need no medium and can travel through vacuum; sound waves are mechanical and need a material medium.
3. EM waves travel at \( 3 \times 10^8 \) m/s in vacuum; sound travels much slower (about 340 m/s in air).
4. EM waves are oscillations of electric and magnetic fields; sound waves are oscillations (compressions and rarefactions) of the particles of the medium.

\[\boxed{E_y = E_0\sin(kx-\omega t),\quad B_z = B_0\sin(kx-\omega t)}\]