A plane electromagnetic wave, has frequency of

Question:

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10} \mathrm{~Hz}$ and its energy density is $1.02 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to

$\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{\mathrm{Nm}^{2}}{\mathrm{C}^{2}}\right.$ and $\quad$ speed $\quad$ of $\quad$ light

$\left.=3 \times 10^{8} \mathrm{~ms}^{-1}\right):$

 

 

  1. $180 \mathrm{nT}$

  2. $160 \mathrm{nT}$

  3. $150 \mathrm{nT}$

  4. $190 \mathrm{nT}$


Correct Option: , 2

Solution:

Energy density $\frac{\mathrm{dU}}{\mathrm{dV}}=\frac{\mathrm{B}_{0}^{2}}{2 \mu_{0}}$

$1.02 \times 10^{-8}=\frac{\mathrm{B}_{0}^{2}}{2 \times 4 \pi \times 10^{-7}}$

$\mathrm{B}_{0}^{2}=\left(1.02 \times 10^{-8}\right) \times\left(8 \pi \times 10^{-7}\right)$

$\mathrm{B}_{0}=16 \times 10^{-8} \mathrm{~T}=160 \mathrm{nT}$

 

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