Question 103: EM waves

Question

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by
E = 20cos(2 $$	imes$$ 10
10
t $$-$$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $$\mu$$
r
= 1)

Accepted Answer

Given, electric field,
E = 20 cos(2 $$	imes$$ 10
10
t $$-$$ 200 x) V/m
Comparing with the standard equation,
E = E
0
cos($$\omega$$t $$-$$ kx) V/m, we get
Wave constant, k = 200
Angular frequency, $$\omega$$ = 2 $$	imes$$ 10
10
rad/s
Speed of the wave, $$v = {\omega  \over k} = {{2 	imes {{10}^{10}}} \over {200}} = {10^8}$$ m/s
Refractive index, $$\mu  = {c \over v} = {{3 	imes {{10}^8}} \over {{{10}^8}}} = 3$$
As we know the relation between the refractive index and dielectric constant,
$$\mu  = \sqrt {{\varepsilon _r}{\mu _r}} $$
Substituting the value in the above equations, we get
$$3 = \sqrt {{\varepsilon _r}(1)} $$
$${\varepsilon _r} = 9$$
Thus, the dielectric constant of the medium is 9.

Answer

9

Answer

2

Answer

$${1 \over 3}$$

Answer

3

EM waves

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20cos(2 $\times 10 10 t - 200x) V/m. The dielectric constant of the medium is equal to : (Take \mu$ r = 1)

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