Question

Explain the equations describing an EM wave.

Answer 1

i. In an EM wave, the magnetic field and electric field both vary sinusoidally with x.

ii. For a wave travelling along X-axis having \(\overset\rightarrow{E}\) along Y-axis and \(\overset\rightarrow{B}\) along the Z-axis,

E_y = E₀ sin (kx – ωt)

B_z = B₀ sin (kx – ωt)

where, E₀ is the amplitude of the electric field (E_y) and B₀ is the amplitude of the magnetic field (B_z).

iii. The propagation constant is given by k = \(\frac{2π}{λ}\) and λ is the wavelength of the wave. The angular frequency of oscillations is given by ω = 2πv, v being the frequency of the wave.

Hence, E_y = E₀ sin (\(\frac{2πx}{λ}– 2πvt)\)

B_z = B₀ sin (\(\frac{2πx}{λ}– 2πvt)\)

v. Both the electric and magnetic fields attain their maximum or minimum values at the same time and at the same point in space, i.e., \(\overset\rightarrow{E}\) and \(\overset\rightarrow{B}\) oscillate in phase with the same frequency.