Question

The frequency of electromagnetic wave in free space is $2$ MHz. When it passes through a region of relative permittivity ${\epsilon }_r=4.0$, then its wave length __________ & frequency ______________.

• A. Becomes double, becomes half
• B. Becomes double, remains constant
• C. Become half, become double
• D. Becomes half, remains constant

Answer 1

The correct option is D Becomes half, remains constant

$c=\frac{1}{\sqrt{{ϵ}_o{\mu }_o}}$

In a dielectric

$v=\frac{1}{\sqrt{{ϵ}_o{ϵ}_r{\mu }_o{\mu }_r}}$

$v=\frac{1}{\sqrt{4{ϵ}_o{\mu }_o}}$

$v=\frac{1}{2\sqrt{{ϵ}_o{\mu }_o}}$

$v=c/2$

Frequency does not change so wavelength should become halved to make velocity half fold.($v=\nu \lambda$)

Hence the correct option is (D).