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# The electric field in an electromagnetic wave is given by $E = 50N/C\: \sin \omega (t-x/c)$. Find the energy contained in a cylinder of cross-section $10cm^2$ and length 50 cm along the x-axis.

$\begin {array} {1 1} (a)\;55 \times 10^{-12}J & \quad (b)\;5.5 \times 10^{-12}J \\ (c)\;55 \times 10^{-10}J & \quad (d)\;5.5 \times 10^{-10}J \end {array}$

Energy density,$U_{av} =\large\frac{1}{2} \in_oE_o^2$
$=\large\frac{1}{2}$$\times 8.85 \times 10^{-12} \times 50^2 = 1.1 \times 10^{-8} J/m^3$
Volume, $V = 10 \times 50 = 5 \times 10^{-4}m^3$
So, energy $= U_{av} \times V = 5.5 \times 10^{-12} J$
Ans : (b)