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

Answer 1

The Correct Option is B

To determine the ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave, we need to understand how the intensity of such a wave is defined.

1. Intensity of an electromagnetic wave is given by the Poynting vector \(\mathbf{S}\), which is the cross product of the electric field (\( \mathbf{E} \)) and the magnetic field (\( \mathbf{B} \)):
2. \(\mathbf{S} = \mathbf{E} \times \mathbf{B}\)
3. For a plane electromagnetic wave, the intensity \( I \) is also related to the magnitudes of the electric field and the magnetic field by:
4. \(I = \frac{1}{2} \epsilon_0 c E^2 = \frac{1}{2} \frac{B^2}{\mu_0} c\)
5. Where \( \epsilon_0 \) is the permittivity of free space, \( \mu_0 \) is the permeability of free space, and \( c \) is the speed of light in vacuum.
6. Since \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \), it implies that the electric field and magnetic field contribute equally to the intensity.
7. This equality leads to a ratio of 1:1 for their contributions to the intensity.

By analyzing the options, we observe:

• Option 1 : 1 states the contributions are equal, aligning with our deductions.
• Option c : 1, 1 : c, and \(1 : c^2\) are incorrect because they imply unequal contributions.

Thus, the correct answer is 1 : 1.