JEE Main · 2022 · 24 Jun 2022 · Shift 2 · EM Waves

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An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of ______ GHz.
(Given

μ_{r} = 1

for dielectric medium)

Answer: 6

Solution

The speed of electromagnetic waves in a dielectric medium is:

c^{'} = \frac{c}{μ _{r} ε _{r}} = \frac{3 \times 1 0 ^{8}}{6.25} = \frac{3 \times 1 0 ^{8}}{2.5} = 1.2 \times 1 0^{8}

m/s

For an antenna, the minimum wavelength is

λ = 4 L

where

L

is the antenna length.

λ = 4 \times 5 \times 1 0^{- 3} = 20 \times 1 0^{- 3}

m

Minimum frequency:

f = \frac{c ^{'}}{λ} = \frac{1.2 \times 1 0 ^{8}}{20 \times 1 0 ^{- 3}} = 6 \times 1 0^{9}

= 6

GHz

Answer: 6

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Integer answer

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