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 to the magnetic field intensity of an EM wave propagating in that medium is

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Solution

Q.
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

$(Given that \sqrt{\frac{μ_{0}}{ε_{0}}} = 120 π)$ [2024]

1 $30 π : 1$

2 $1 : 120 π$

3 $60 π : 1$

4 $120 π : 1$

Ans.
(3)

Given, $\frac{μ_{r}}{ε_{r}} = \frac{1}{4}$

From $c = \frac{1}{\sqrt{μ ε}} and c = \frac{E}{B}$

$\frac{1}{\sqrt{μ ε}} = \frac{E}{B}$ ...(i) and $B = μ H$ ...(ii)

Putting (ii) in equation (i), we get

$\frac{E}{μ H} = \frac{1}{\sqrt{μ ε}}$

$∴$ $\frac{E}{H} = \frac{μ}{\sqrt{μ ε}} = \sqrt{\frac{μ}{ε}} = \sqrt{\frac{μ_{0} μ_{r}}{ε_{0} ε_{r}}}$

$= \sqrt{\frac{μ_{0}}{ε}} \sqrt{\frac{μ_{r}}{ε_{r}}} = 120 π \times \sqrt{\frac{1}{4}} = \frac{120 π}{2} = 60 π$

$∴$ $E : H = 60 π : 1$

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