Question

In the EM wave the amplitude of the magnetic field $ {H_0} $ and the amplitude of the electric field $ {E_0} $ in free space place are related as:
(A) $ {H_0} = {E_0} $
(B) $ {H_0} = \dfrac{{{E_0}}}{c} $
(C) $ {{H}_{0}}={{E}_{0}}\sqrt{{{\mu }_{0}}{{\epsilon }_{0}}} $
(D) $ {{H}_{0}}={{E}_{0}}\sqrt{\dfrac{{{\epsilon }_{0}}}{{{\mu }_{0}}}} $

Answer 1

Hint
For an electromagnetic wave, the ratio of the amplitude of the electric field and the magnetic field is equal to the speed of light. Rearrange the aforementioned relation to match with one of the options.

Complete step by step answer
We know that for an electromagnetic wave, the speed of light is defined as the ratio of the amplitude of the electric field to the amplitude of the electric field. Since we’ve been given the amplitude of the magnetic field as $ {H_0} $ and the amplitude of the electric field as $ {E_0} $, we can calculate the speed of light as:
 $ c = \dfrac{{{E_0}}}{{{H_0}}} $
On rearranging the above equation, we \get:
$ {H_0} = \dfrac{{{E_0}}}{c} $ which corresponds to option (B).

Additional Information
Light waves travel in the form of electromagnetic waves so we can assume that all electromagnetic waves travel at the speed of light in a given medium. In an electromagnetic wave, the electric field and magnetic field are perpendicular to each other and the direction of their cross product gives us the direction of propagation of the electromagnetic wave. And the ratio of their amplitudes gives us information about the speed of light in the medium.

Note
Since we’ve been given that the electromagnetic wave is propagating in free space so we can assume the speed of the electromagnetic wave as $ c $ which would have been lower if the wave was travelling in a medium. Checking the dimensional formula of different options can also help us since the dimensional formula of the terms on the right-hand side of option (A), (C) and (D) don’t have the dimensions of the amplitude of the magnetic field.