Correct Answer - Option 1 :
\({\left( {\frac{{{\mu _0}}}{{{\varepsilon _0}}}} \right)^{\frac{1}{2}}}\)
Intrinsic Impedance of Free space:
- The electromagnetic wave or EM wave is a special kind of wave which do not require any material medium for its propagation.
- As the name suggested it is a combination of the time-varying oscillating electric and magnetic field which propagates in a space with a speed very close to the speed of light.
- EM waves are formed when the electric and magnetic field comes in contact and oscillates perpendicular to each other.
- The direction of propagation of EM is perpendicular to that of the oscillating electric and magnetic field. Therefore it falls in the category of a transverse wave.
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EM waves are solutions of Maxwell's equation which are the fundamental equations of electrodynamics.
- The Intrinsic Impedance (v)of the wave is defined as the ratio of electric field E and magnetic field B of a given medium.
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It is denoted by \(\eta \) . so, we can Intrinsic Impedance in terms of the electric and magnetic field as: \(\eta =\frac{E}{H}\)
From Maxwell's equations, we have
\(\frac{E}{B}=v\) ...(1) and
\(v=\frac{1}{\sqrt{\mu_0 \varepsilon_0 }}\) ....(2)
Where,
E is the electric field in a given medium
B is the magnetic field in a given medium
\(\mu \) is the permeability of the medium and
v is the speed of light waves in the same medium.
From magnetism, we have
\(B=\mu H\) ...(3)
Using equation (2) and (3) in equation (1), we get
\(\frac{E}{\mu _0H}=\frac{1}{\sqrt{\mu_0 \varepsilon_0 }}\)
\(\Rightarrow \frac{E}{H}=\frac{\mu_0 }{\sqrt{\mu_0 \varepsilon_0 }}=\eta \)
\(\therefore \eta =\sqrt{\frac{\mu_0 }{\varepsilon_0 }}\)
