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

In an electromagnetic wave, the ratio of electric field intensity (E) to magnetic field intensity (H) in a medium is given by:

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

Given that $\sqrt{\frac{\mu_0}{\epsilon_0}} = 120\pi$ and $\frac{\mu_r}{\epsilon_r} = \frac{1}{4}$:

$\frac{E}{H} = 120\pi \sqrt{\frac{1}{4}} = 60\pi$

Thus, the ratio of E to H is 60π : 1.