
If refractive index and dielectric constant of the material of a glass slab is and respectively then magnetic permeability of the glass is (in S.I. system)
A.
B.
C.
D.
Answer
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Hint: The expression of relative permeability of glass in terms of its refractive index and dielectric constant will be used to calculate its value. We will also use the expression for magnetic permeability in terms of its relative permeability and permeability of free space.
Complete step by step answer:
Given:
The refractive index of the material of the glass slab is .
The dielectric constant of the material of the glass slab is .
We have to find the magnetic permeability of the material of glass in the S.I. system.
The glass's refractive index is equal to the square root of the product of relative permeability and dielectric constant of glass.
Here is the relative permeability of glass.
Substitute for n and for in the above expression.
……(1)
On squaring both sides of equation (1), we get:
We know that relative permeability is the ratio of magnetic permeability of glass to free space's magnetic permeability.
Here is the magnetic permeability in free space, and its value is given below.
Substitute for and for in the above expression to get the value of magnetic permeability of glass.
We also know that the S.I. unit of magnetic permeability of a substance is .
The value of magnetic permeability calculated above is nearly equal to option (4). Therefore, the magnetic permeability of the given glass slab having a refractive index and dielectric constant is
So, the correct answer is “Option D”.
Note:
We have to note that the value of magnetic permeability is asked, so do not just calculate the relative permeability. Also, substitute the value of magnetic permeability in free space in its S.I. because the final answer is asked in its S.I. system.
Complete step by step answer:
Given:
The refractive index of the material of the glass slab is
The dielectric constant of the material of the glass slab is
We have to find the magnetic permeability of the material of glass in the S.I. system.
The glass's refractive index is equal to the square root of the product of relative permeability and dielectric constant of glass.
Here
Substitute
On squaring both sides of equation (1), we get:
We know that relative permeability is the ratio of magnetic permeability of glass to free space's magnetic permeability.
Here
Substitute
We also know that the S.I. unit of magnetic permeability of a substance is
The value of magnetic permeability calculated above is nearly equal to option (4). Therefore, the magnetic permeability of the given glass slab having a refractive index
So, the correct answer is “Option D”.
Note:
We have to note that the value of magnetic permeability is asked, so do not just calculate the relative permeability. Also, substitute the value of magnetic permeability in free space in its S.I. because the final answer is asked in its S.I. system.
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