Question

The wave impedance of free space is
A) $37.6\mathrm{\Omega }$
B) $376.6\mathrm{\Omega }$
C) $33.66\mathrm{\Omega }$
D) $3.76\mathrm{\Omega }$

Answer 1

Hint: The wave impedance will relate the electric field and magnetic field of the signals. It is the ratio of both the components. The wave impedance is different in many cases.

Complete step by step answer:
The ratio of the electric and magnetic components of the electromagnetic waves is the wave impedance. In fact it is the intrinsic impedance of the medium. Hence the wave impedance of the electromagnetic wave is the same everywhere in the intrinsic medium. The expression for the wave impedance is given as,
$Z={\displaystyle \frac{E}{H}}$
Where, $E$ is the electric field component of the EM wave. It is measured in volts per meter. And $H$ is the magnetic field component of the EM wave. It is measured in amperes per meter.
Now, let’s look about the wave impedance in free space. In free space the electromagnetic wave would not be obstructed by anything. Thus it travels at the speed of light.
The value of permittivity of free space is given as,
${\epsilon }_0={\displaystyle \frac{{10}^9}{36\pi }}$
And let’s learn about the permeability. Permeability is the constant used in electromagnetism.
The value of permeability in free space is given as,
${\mu }_0=4\pi \times {10}^7$
The expression for the wave impedance in free space is given as,
$Z=\sqrt{{\displaystyle \frac{{\epsilon }_0}{{\mu }_0}}}$
Substituting the values in the above expression gives,
$$\begin{gathered} Z=\sqrt{{\displaystyle \frac{{\displaystyle \frac{{10}^9}{36\pi }}}{4\pi \times {10}^7}}} \\ =376.7\mathrm{\Omega } \end{gathered}$$
Hence the wave impedance of the free space is $376.7\mathrm{\Omega }$.
The answer is option B.

Note: The permittivity of the free space denotes how the material gets polarized when the electric field is applied. And permeability denotes the energy stored in the magnetic field.