Question 183: EM waves

Question

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ $$	imes$$ 10
$$-$$2
cm.

Accepted Answer

Given, frequency of wave, f = 3 GHz = 3 $$	imes$$ 10
9
Hz
Relative permittivity, $$\varepsilon $$
r
= 2.25
Since, f = C/$$\lambda$$
$$ \Rightarrow \lambda  = {c \over f} = {{3 	imes {{10}^8}} \over {3 	imes {{10}^9}}} = 0.1$$ m
$$\because$$ $$\lambda$$
m
(wavelength of wave in a medium) = $$\lambda$$/$$\mu$$ and we know that, $$\mu  = \sqrt {{\mu _r}{\varepsilon _r}} $$
As, dielectric is non-magnetic, $$\mu$$
r
= 1
$$ \Rightarrow \mu  = \sqrt {2.25}  = 1.5$$
$$ \Rightarrow {\lambda _m} = {{0.1} \over {1.5}} = {1 \over {15}} = 0.0667$$ m
= 6.67 cm = 667 $$	imes$$ 10
$$-$$2
cm

EM waves

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ $\times 10 -$2 cm.

Integer / Numeric Answer Type