First slide

Electromagnetic waves and its nature

Question

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10} H z$ 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
$(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} \frac{N m^{2}}{C^{2}} a n d s p e e d o f l i g h t = 3 \times 10^{8} m s^{- 1})$ :

Moderate

A

190nT
B

180nT
C

160nT
D

150nT

Solution

$\begin{array}{l} E n e r g y d e n s i t y = \frac{B_{0}^{2}}{2 μ_{0}} = \frac{B_{0}^{2} \in_{0}}{2 μ_{0} \in_{0}} = \frac{B_{0}^{2} C^{2} \in_{0}}{2} a s (C^{2} = \frac{1}{μ_{0} \in_{0}}) \\ \Rightarrow B_{0} = \frac{1}{C} \sqrt{\frac{2 (Energy density)}{\in_{0}}} \\ \Rightarrow B_{0} = \frac{1}{3 \times 10^{8}} \sqrt{\frac{2 \times 1.02 \times 10^{- 8}}{4 π \in_{0}} 4 π} \\ = \frac{1}{3 \times 10^{8}} \sqrt{2 \times 1.02 \times 10^{- 8} \times 9 \times 10^{9} \times 4 π} = 160.11 \times 10^{- 9} T \end{array}$

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