(a) Write the expression for the speed of light in a material medium of relative permittivity $\varepsilon_r$ and relative magnetic permeability $\mu_r$. (b) Write the wavelength range and name of the electromagnetic waves which are used in (i) radar systems for aircraft navigation, and (ii) Earth satellites to observe the growth of crops.

(a) $v = \dfrac{1}{\sqrt{\mu_0\mu_r\,\varepsilon_0\varepsilon_r}} = \dfrac{c}{\sqrt{\mu_r\varepsilon_r}}$. (b)(i) Microwaves, $\sim10^{-3}$--$10^{-1}$ m; (ii) Infrared, $\sim700$ nm--1 mm.

CBSE Class 12 · 2020 · EM WavesShort Answer

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(a) Write the expression for the speed of light in a material medium of relative permittivity

ε_{r}

and relative magnetic permeability

μ_{r}

.
(b) Write the wavelength range and name of the electromagnetic waves which are used in (i) radar systems for aircraft navigation, and (ii) Earth satellites to observe the growth of crops.

Solution

(a) In a medium of permittivity

ε = ε_{0} ε_{r}

and permeability

μ = μ_{0} μ_{r}

, the speed of light is

v = \frac{1}{μ ε} = \frac{1}{μ _{0} μ _{r} ε _{0} ε _{r}} = \frac{c}{μ _{r} ε _{r}}

(b)(i) RADAR for aircraft navigation uses microwaves, wavelength range about

1 0^{- 3}

m to

1 0^{- 1}

m.
(ii) Observing crop growth from Earth satellites uses infrared waves, wavelength range about 700 nm to 1 mm.

v = c / μ_{r} ε_{r}; (i) microwaves, (ii) infrared

CBSE Class 12 Board · 2020 · Subjective

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CBSE Class 12 · 2020 · EM WavesShort Answer

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