Question

The amplitudes ${E_0}$ and ${B_0}$ ​ of electric and the magnetic component of an electromagnetic wave respectively are related to the velocity c in vacuum as
A. ${E_0}{B_0} = \dfrac{1}{c}$
B. ${E_0} = \dfrac{c}{{{B_0}}}$
C. ${B_0} = c{E_0}$
D. ${E_0} = c{B_0}$
E. ${E_0} = {c^3}{B_0}$

Answer 1

Hint: Electric field amplitude and magnetic field amplitude are given here because the magnetic field and electric field exist in the electromagnetic wave and light is also an EM wave and the direction of propagation of light and oscillations of magnetic field particles and electric field particles are mutually perpendicular.

Complete step by step answer:
There are two kinds of waves normally. One will be a transverse wave and the other will be a longitudinal wave. In case of transverse waves the direction of propagation of waves is perpendicular to the direction of vibration of the particles of the medium. Transverse wave has crests and troughs. In case of the longitudinal wave particles of the medium of propagation vibrates in the direction of propagation of the wave. This longitudinal wave has compressions and rarefactions. In case of longitudinal waves particles vibrate in to and fro motion. Transverse waves can propagate without medium too whereas longitudinal waves require medium to propagate. Example for transverse wave is light whereas example for the longitudinal wave is sound.
Light is an electromagnetic wave which is transverse in nature where the phase of the magnetic field and the electric field will be the same for this EM wave.
Light is a form of energy which is stored in the small packets like structures called photons which travel with the same speed of light.
We have
$\dfrac{{{E_0}}}{{{B_0}}} = c$
${E_0} = c{B_0}$

So, the correct answer is “Option D”.

Note: If we don’t know the exact formula we can also solve this by dimensional method. We have the magnetic force acting on the charge which moves with velocity in the magnetic field and force acting on the charge due to the electric field and if we take the ratio of electric field and magnetic field from these expressions we get the velocity.