Ncert Exercises & Solutions

The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is:

1. c : 1

2. $c^{2}$ : 1

3. 1 : 1

4. $\sqrt{c}$ : 1

(c)

Hint: The energies of the electric field and the magnetic field are equal to each other in an electromagnetic wave.

Step 1: Find the energies of the electric field and the magnetic field.

Intensity in terms of electric field, U_{av} = \frac{1}{2} ε_{0} E_{0}^{2}

intensity in terms of magnetic field, U_{av} = \frac{B_{0}^{2}}{2 μ_{0}}

Now taking the intensity in terms of electric field,

{(U_{av})}_{electric field} = \frac{1}{2} ε_{0} E_{0}^{2}

\Rightarrow = \frac{1}{2} ε_{0} {({cB}_{0})}^{2} (∵ E_{0} = {cB}_{0})

= \frac{1}{2} ε_{0} \times c^{2} B^{2}

But, c = \frac{1}{\sqrt{μ_{0} ε_{0}}}

∴ {(U_{av})}_{electric field} = \frac{1}{2} ε_{0} \times \frac{B^{2}}{μ_{0} ε_{0}} = {(U_{av})}_{magnetic field}

Step 2: Find the ratio of intensities.

Thus, the energy in the electromagnetic wave is divided equally between the electric field vector and the magnetic field vector.
Therefore, the ratio of contributions by the electric field and magnetic field components to the intensity of an electromagnetic wave is 1: 1.

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