Question

According to Maxwell's theory the value of $\sqrt {\dfrac {1}{{\mu}_{0}{\epsilon}_{0}}}$ for free space represents:
A.Wave length in any medium
B.Frequency of light
C.Speed of light in vacuum
D.Dual nature of light

Answer 1

Hint: While solving Maxwell’s electromagnetic equations, we derive two sine wave equations. These equations have $\mu$ and $\epsilon$ constant. While solving these constants, a value was obtained which showed the property of light. It also proved that light is an electromagnetic wave.

Complete answer:
From Maxwell's electromagnetic field equations, we can derive equations for electric and magnetic fields. These equations have $\mu$ and $\epsilon$ which are used as constants. These constants are related to each other by,
$v= \sqrt {\dfrac {1}{{\mu}_{0}{\epsilon}_{0}}}$
Where, $v$ is the speed of wave
              ${\mu}_{0}$ is the permeability of free space
              ${\epsilon}_{0}$ is the absolute permittivity of free space
The above mentioned mathematical equation shows a relation between electricity and magnetism.
Later, experimentally it was found that the value of v is nearly equal to $3\times {10}^{8}$. Hence, it was found that the above fraction had a value equal to speed of light. So, it can be inferred that speed of light is inversely proportional to the square root of permittivity of free space.

Hence, the correct answer is option C i.e. speed of light.

Note:
- ${\epsilon}_{0}$ is a physical quantity which represents the capability of vacuum or air to permit electric fields. Hence, it is known as the absolute permittivity of free space or vacuum or air.
- ${\mu}_{0}$ is a quantity which represents the amount of resistance experienced while forming a magnetic field in vacuum. It is called permeability of free space, permeability of vacuum, magnetic constant, etc.