Question

If the ratio of relative permeability and relative permittivity of a uniform medium is \(1 : 4\). The ratio of the magnitudes of electric field intensity (\(E\)) to the magnetic field intensity (\(H\)) of an EM wave propagating in that medium is:
\[ \text{Given that } \sqrt{\frac{\mu_0}{\epsilon_0}} = 120 \pi : \]

• A. \(30\pi : 1\)
• B. \(1 : 120\pi\)
• C. \(60\pi : 1\)
• D. \(120\pi : 1\)

Answer 1

The Correct Option is C

Intrinsic impedance of a medium: 

In an electromagnetic wave, the ratio of electric field intensity $E$ to magnetic field intensity $H$ is:

$$ \frac{E}{H} = \sqrt{\frac{\mu}{\epsilon}} $$

Where $\mu$ = permeability and $\epsilon$ = permittivity of the medium.

$$ \frac{E}{H} = \sqrt{\frac{\mu_r \mu_0}{\epsilon_r \epsilon_0}} = \sqrt{\frac{\mu_0}{\epsilon_0}} \sqrt{\frac{\mu_r}{\epsilon_r}} $$

Given:

$$ \sqrt{\frac{\mu_0}{\epsilon_0}} = 120\pi \, \Omega \quad \text{(impedance of free space)} $$ $$ \frac{\mu_r}{\epsilon_r} = \frac{1}{4} $$

Substituting the values:

$$ \frac{E}{H} = 120\pi \times \sqrt{\frac{1}{4}} $$ $$ \frac{E}{H} = 120\pi \times \frac{1}{2} $$ $$ \frac{E}{H} = 60\pi \, \Omega $$

Thus, the ratio of E to H is $60\pi : 1$