First slide

Electromagnetic waves and its nature

Question

The electric field of plane electromagnetic wave of amplitude 2V/m varies with time, propagating along z-axis. The average energy density of magnetic field $(in J / m^{3})$ is equal to $x \times 10^{- 12} J / m^{3}$ . Then ‘x’ value is equal to ( $\in_{0} = 8.854 \times 10^{- 12} F / m$ )

Moderate

Solution

For an electro magnetic wave ,Average energy density due to electric field
=Average energy density due to magnetic field
$\begin{array}{l} = \frac{1}{4} ε_{0} E_{0}^{2} \\ = \frac{1}{4} \times 8.85 \times 10^{- 12} \times 2 \times 2 \end{array}$
$\begin{array}{l} = 8.85 \times 10^{- 12} Joule m^{- 3} \\ = x \times 10^{- 12} Joule m^{- 3} \end{array}$
$∴ x = 8.85$

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