A plane electromagnetic wave, has frequency of 2 . 0 × 10 ^ 10 Hz and its energy density is 1 . 02 × 10 ^ - 8 J m ^ - 3 in vacuum. The amplitude of the magnetic field of the wave is close to ( 1 4 π ε _ 0 = 9 × 10 ^ 9

Correct answer: B. 160nT Energy Denisty = (1)/(2) B ^ 2 μ _ 0 B = 2 × μ _ 0 × Energy density B = 2 × 4π × 10 ^ - 7 × 1 . 02 × 10 ^ - 8 = 160 × 10 ^ - 9 = 160nT

JEE Main 20202 SeptemberMorning Shift

Exam: JEE Main
Year: 2020
Date: 2 September
Shift: Morning Shift
Subject: Physics
Chapter: Electromagnetic Waves

JEE Main 2020 · 2 September · Morning Shift · Physics · Electromagnetic Waves

A plane electromagnetic wave, has frequency of 2 . 0 × 10 ^ 10 Hz...

A plane electromagnetic wave, has frequency of

2 . 0 \times {10}^{10}Hz

and its energy density is

1 . 02 \times {10}^{- 8}J{m}^{- 3}

in vacuum. The amplitude of the magnetic field of the wave is close to

\left(\dfrac{1}{4{\pi ε}_{0}} = 9 \times {10}^{9}\dfrac{{Nm}^{2}}{{C}^{2}}\right)

and speed of light

= 3 \times {10}^{8}m{s}^{- 1}

Options

A $150nT$
B $160nT$
C $180nT$
D $190nT$

Correct answer

B. $160nT$

Step-by-step solution

Energy Denisty $= \dfrac{1}{2}\dfrac{{B}^{2}}{{\mu}_{0}}$

$B = \sqrt{2 \times {\mu}_{0} \times \text{Energy density}}$

$B = \sqrt{2 \times 4\pi \times {10}^{- 7} \times 1 . 02 \times {10}^{- 8}} = 160 \times {10}^{- 9} = 160nT$

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