First slide

Nature of electromagnetic wave

Question

An electromagnetic wave of frequency 3 MHz passes from Vacuum into a dielectric medium with relative permittivity $\in_{r}$ = 4.0 Then

Difficult

A

wave length doubled and frequency remains unchanged
B

wave length is doubled and frequency becomes half
C

wave length is halved and frequency remains unchanged
D

wave length and frequency both remain unchanged

Solution

Frequency of EM wave does not change in medium but wave length and velocity of wave changes.
In vacuum, $C = \frac{1}{\sqrt{μ_{0} ε_{0}}} = f λ_{vaccum}$
In medium, $C_{med} = \frac{1}{\sqrt{μ_{0} μ_{r} ε_{0} ε_{r}}} = \frac{C}{\sqrt{μ_{r} ε_{r}}}$
For dielectric medium, $μ_{r} = 1$
$\begin{array}{rcl} C_{med} & = & \frac{C}{\sqrt{ε_{r}}} = \frac{C}{2} (∴ ε_{r} = 4) \\ λ_{med} & = & \frac{C_{med}}{f} = \frac{C}{2 f} = \frac{λ_{vaccum}}{2} \end{array}$

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