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An electromagnetic wave of frequency $1\times10^{14}\, hertz$ is propagating along $z-$ axis. The amplitude of electric field is $4\, V/m$ . lf ${\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2$ , then average energy density of electric field will be:
$35 .2\times10^{-10}\, J/m^3$
$35 .2\times10^{-11}\, J/m^3$
$35 .2\times10^{-12}\, J/m^3$
$35 .2\times10^{-13}\, J/m^3$
Solution
Given: Amplitude of electric field,
$E_{0}=4\,\mathrm{v} / \mathrm{m}$
Absolute per mitivity,
$\varepsilon_{0}=8.8 \times 10^{-12}\, \mathrm{c}^{2}\, / \mathrm{N}-\mathrm{m}^{2}$
Average energy density $u_{E}=?$
Applying formula,
Average energy density $u_{E}=\frac{1}{4} \varepsilon_{0} E^{2}$
$\Rightarrow u_{E}=\frac{1}{4} \times 8.8 \times 10^{-12} \times(4)^{2}$
$=35.2 \times 10^{-12} \,\mathrm{J} / \mathrm{m}^{3}$
