Question

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is :
$(c=$ speed of electromagnetic waves$)$

• A. $1:c$
• B. $1$ : $c^2$
• C. $c$ : $1$
• D. $1$ : $1$

Answer 1

The correct option is D $1$ : $1$

Intensity of electromagnetic wave, $I=U_{\text{avg}}c$
In terms of electric field, $U_{\text{avg}}=\frac{1}{2}{ϵ}_o{E}_o^2$

In terms of magnetic field, $U_{\text{avg}}=\frac{1}{2}\frac{B_o^2}{{\mu }_o}$
$(\because E_o=c{B}_0)$
Now $U_{\text{avg}}$ $\left(\text{due to electric field}\right)$ $=\frac{1}{2}{ϵ}_o\left(c{B}_o^2\right)=\frac{1}{2}{ϵ}_o\times \frac{1}{{\mu }_o{ϵ}_o}{B}_o^2$
$=\frac{1}{2}\frac{B_o^2}{{\mu }_o}=U_{\text{avg}}\left(\text{due to the magnetic field}\right)$
The energy distribution in electric and magnetic fields are equal.

Therefore, the ratio of contributions by the electric field and magnetic field components to the intensity of electromagnetic wave is $1:1$