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The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is
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1757 Upvotes
Verified Answer
The correct answer is:
$1: 1$
$1: 1$
Intensity in terms of electric field
$$
\mathrm{U}_{\mathrm{av}}=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2
$$
Intensity in terms of magnetic field
$$
\mathrm{U}_{\mathrm{av}}=\frac{1}{2} \frac{\mathrm{B}_0^2}{\mu_0}
$$
We also know that the relationship between $\mathrm{E}$ and $\mathrm{B}$ is
$$
\mathrm{E}_0=\mathrm{cB}_0
$$
So the average energy by electric field is
$$
\begin{aligned}
&\begin{aligned}
\left(\mathrm{U}_{\mathrm{av}}\right)=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2=\frac{1}{2} \varepsilon_0 \mathrm{E}_0\left(\mathrm{cB}_0\right)^2 \\
=& \frac{1}{2} \varepsilon_0 \times \mathrm{c}^2 \mathrm{~B}^2 \\
\therefore \quad\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Electric field }} &=\frac{1}{2} \varepsilon_0 \times \frac{1}{\mu_0 \varepsilon_0} \mathrm{~B}_0^2 \\
&=\frac{1}{2} \frac{\mathrm{B}_0^2}{\mu_0}=\left(\because \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\right)
\end{aligned} \\
&\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Magnetic field }}
\end{aligned}
$$
So, the energy in electromagnetic wave is divided equally between electric field vector and magnetic field vector. Then, the ratio of contributions by the electric field and magnetic field components to the intensity of an electromagnetic wave is
$$
\text { Ratio }=\frac{\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {electric field }}}{\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Magnctic field }}}=1: 1
$$
$$
\mathrm{U}_{\mathrm{av}}=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2
$$
Intensity in terms of magnetic field
$$
\mathrm{U}_{\mathrm{av}}=\frac{1}{2} \frac{\mathrm{B}_0^2}{\mu_0}
$$
We also know that the relationship between $\mathrm{E}$ and $\mathrm{B}$ is
$$
\mathrm{E}_0=\mathrm{cB}_0
$$
So the average energy by electric field is
$$
\begin{aligned}
&\begin{aligned}
\left(\mathrm{U}_{\mathrm{av}}\right)=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2=\frac{1}{2} \varepsilon_0 \mathrm{E}_0\left(\mathrm{cB}_0\right)^2 \\
=& \frac{1}{2} \varepsilon_0 \times \mathrm{c}^2 \mathrm{~B}^2 \\
\therefore \quad\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Electric field }} &=\frac{1}{2} \varepsilon_0 \times \frac{1}{\mu_0 \varepsilon_0} \mathrm{~B}_0^2 \\
&=\frac{1}{2} \frac{\mathrm{B}_0^2}{\mu_0}=\left(\because \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\right)
\end{aligned} \\
&\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Magnetic field }}
\end{aligned}
$$
So, the energy in electromagnetic wave is divided equally between electric field vector and magnetic field vector. Then, the ratio of contributions by the electric field and magnetic field components to the intensity of an electromagnetic wave is
$$
\text { Ratio }=\frac{\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {electric field }}}{\left(\mathrm{U}_{\mathrm{av}}\right)_{\text {Magnctic field }}}=1: 1
$$
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