# The magnetic field in a plane electromagnetic wave is given by $B = 100\mu T \sin [(2 \times10^{15}s^{-1}) (t-x/c)]$. Calculate the average energy density corresponding to the electric field.

$\begin {array} {1 1} (a)\;3.98 \times 10^{-3}J/m^3 & \quad (b)\;39.8 \times 10^{-3}J/m^3 \\ (c)\;39.8 \times 10^{-5}J/m^3 & \quad (d)\;3.98 \times 10^{-5}J/m^3 \end {array}$

## 1 Answer

$E_o = B_oc = 100 \times 10^{-6} \times 3 \times 10^8 = 300 \times 10^2V/m$
Average energy density $= \large\frac{1}{2} $$\in_oE_o2 = \large\frac{1}{2}$$\times 8.85 \times 10^{-12} \times (300 \times 10^2)^2$
$= 3.98 \times 10^{-3}J/m^3$
Ans : (a)
answered Mar 1, 2014

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