Question

For a medium with permittivity $\varepsilon $ and permeability $\mu $ , the velocity of light is given by;
A. $\dfrac{\varepsilon }{{\sqrt \mu }}$
B. $\sqrt {\mu \varepsilon } $
C. $\dfrac{1}{{\sqrt {\mu \varepsilon } }}$
D. $\dfrac{\varepsilon }{{\sqrt \mu }}$

Answer 1

Hint: In this question, we will know the basic information about the permittivity and permeability and this will help us find the correct result. Further, the basic information will help us for our better understanding.

Formula used:
$c = \dfrac{1}{{\sqrt {\mu \varepsilon } }}$

Complete step by step solution:
As we know that the velocity of electromagnetic radiation is the velocity of light, which is denoted by c.
There is a direct relation between the permittivity $\varepsilon $ and permeability $\mu $ with the velocity of light, which is given by:
$c = \dfrac{1}{{\sqrt {\mu \varepsilon } }}$
Therefore, we get the required result and the correct option is C) i.e., for a medium having permittivity and permeability the value of the velocity of light is given by the above equation.

So, the correct answer is “Option C”.

Additional Information: Here, we can define permittivity as the property of material, which measures the opposition offered against the formation of an electric field. It gives information about the number of charges required to generate one unit of electric flux in the given medium. Also, mathematically it can be expressed as the ratio of electric displacement and electric field intensity. The S.I unit of permittivity is Farad per meter. The main application of this is in a capacitor.
Now we see that permeability is defined as the measure of the ability of the material to allow the formation of magnetic field lines of force or magnetic field within. It gives the ability of magnetization that a material possesses for the applied magnetic field. Mathematically, it is given by the ratio of magnitude of magnetic induction (B) and intensity of magnetic field (H). The S.I unit of permeability is Henry per meter. The main application of this is in transformer cores and inductors.

Note: We should remember the difference between the permittivity and permeability that the permittivity is related to the formation of an electric field, and the permeability is because of the magnetic field. Further, we should know that the velocity of light is $3 \times {10^8}m/s$.