Question

The relation between permittivity of free space, the permeability of free space and speed of light is:

• A. \( \epsilon_0 \mu_0 = \frac{4\pi}{c^2} \)
• B. \( \epsilon_0 \mu_0 = \frac{1}{c^2} \)
• C. \( \epsilon_0 \mu_0 = \frac{1}{c} \)
• D. \( \epsilon_0 \mu_0 = c^2 \)

Hint:

Remember that the relationship \( \epsilon_0 \mu_0 = \frac{1}{c^2} \) is essential in understanding the properties of electromagnetic waves and is fundamental to Maxwell's equations.

Answer 1

The Correct Option is B

The relation between permittivity (\( \epsilon_0 \)) and permeability (\( \mu_0 \)) of free space, and the speed of light \( c \) is given by the following equation: \[ \epsilon_0 \mu_0 = \frac{1}{c^2} \] This is a fundamental equation in electromagnetism, linking the speed of light to the properties of free space. - Option (1) is incorrect because the relation involves \( \frac{1}{c^2} \) rather than \( \frac{4\pi}{c^2} \). - Option (2) is correct, as \( \epsilon_0 \mu_0 = \frac{1}{c^2} \) is the correct relation. - Option (3) is incorrect, as the equation does not involve \( \frac{1}{c} \). - Option (4) is also incorrect because \( \epsilon_0 \mu_0 \) is not equal to \( c^2 \). Thus, the correct answer is option (2), \( \epsilon_0 \mu_0 = \frac{1}{c^2} \).

Answer 2

Step 1: Understanding permittivity and permeability of free space
The permittivity of free space, \( \epsilon_0 \), measures how much electric field can permeate the vacuum.
The permeability of free space, \( \mu_0 \), measures the ability of vacuum to support the formation of magnetic fields.

Step 2: Speed of light in vacuum
The speed of light, \( c \), in vacuum is related to these two constants because electromagnetic waves propagate through vacuum governed by electric and magnetic fields.

Step 3: Mathematical relation
From Maxwell’s equations, the speed of electromagnetic waves is given by:
\[ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \]
Squaring both sides:
\[ c^2 = \frac{1}{\epsilon_0 \mu_0} \]
Rearranging:
\[ \epsilon_0 \mu_0 = \frac{1}{c^2} \]

Step 4: Conclusion
Thus, the relation between permittivity of free space, permeability of free space, and speed of light is:
\[ \epsilon_0 \mu_0 = \frac{1}{c^2} \]