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Chapter 20: Problem 2737

Wave impedance of free space is (A) Zero (B) \(376.6 \Omega\) (C) \(33.6 \Omega\) (D) \(3.76 \Omega\)

Short Answer

Expert verified
The wave impedance of free space is \(376.6 \Omega\).

Step by step solution

01

Write the Formula for Wave Impedance

We will start by writing the formula for wave impedance: Wave Impedance, Z = \(\sqrt{\cfrac{\mu_0}{\epsilon_0}}\)
02

Substitute the Values of Magnetic Permeability and Electric Permittivity of Free Space

Now, we will substitute the given values of magnetic permeability and electric permittivity of free space: \(\mu_0 = 4\pi \times 10^{-7} \ H/m\) \(\epsilon_0 = 8.854 \times 10^{-12} \ F/m\) Z = \(\sqrt{\cfrac{(4\pi \times 10^{-7} \ H/m)}{(8.854 \times 10^{-12} \ F/m)}}\)
03

Calculate the Wave Impedance of Free Space

Now, perform the calculation: Z = \(\sqrt{\cfrac{(4\pi \times 10^{-7})}{(8.854 \times 10^{-12})}} \Omega\) Z = \(376.6 \Omega\)
04

Compare the Result with the Given Options

Compare the result to the given options: (A) Zero (B) \(376.6 \Omega\) (C) \(33.6 \Omega\) (D) \(3.76 \Omega\) The wave impedance of free space matches the value given in option (B). Therefore, the correct answer is: \(Z = 376.6 \Omega\).

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