Intrinsic Impedance of Free Space Explained

The intrinsic impedance of a medium, often denoted by $Z$, represents the ratio of the electric field strength ($E$) to the magnetic field strength ($H$) for a plane wave traveling in that medium. It's a fundamental property related to how electromagnetic waves propagate through a material.

Calculating Free Space Impedance

For free space (vacuum), the intrinsic impedance ($Z_0$) depends on two fundamental physical constants:

• The permeability of free space, denoted as $\mu_0$. Its value is exactly $4\pi \times 10^{-7} \, \text{H/m}$ (Henry per meter).
• The permittivity of free space, denoted as $\epsilon_0$. Its value is approximately $8.854 \times 10^{-12} \, \text{F/m}$ (Farad per meter).

The formula to calculate the intrinsic impedance of free space is:

$$ Z_0 = \sqrt{\frac{\mu_0}{\epsilon_0}} $$

Let's substitute the values:

$$ Z_0 = \sqrt{\frac{4\pi \times 10^{-7} \, \text{H/m}}{8.854 \times 10^{-12} \, \text{F/m}}} $$

Calculating this value gives:

$$ Z_0 \approx \sqrt{1.419 \times 10^{5}} \, \Omega $$

$$ Z_0 \approx 376.73 \, \Omega $$

Understanding the Result

This calculated value is very close to 377 Ohms. In many practical applications and theoretical contexts within electromagnetics and electrical engineering, the intrinsic impedance of free space is commonly approximated and referred to as 377 $\\Omega$. This value is crucial when analyzing radio wave propagation, antenna design, and transmission lines in free space.

Comparing this to the options provided:

• 75 $\\Omega$ is the approximate impedance of a standard coaxial cable (like RG-6).
• 73 $\\Omega$ is the approximate impedance of another type of coaxial cable (like RG-59).
• 120 $\\Omega$ is related to the characteristic impedance of a dipole antenna but is not the intrinsic impedance of free space.
• 377 $\\Omega$ matches our calculated and commonly used value for the intrinsic impedance of free space.

Therefore, the correct intrinsic impedance of free space is approximately 377 $\\Omega$.