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Electromagnetic Waves — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectromagnetic Waves3 Marks
Question
The magnetic field in a plane electromagnetic wave is given by $\text{B}=(200\mu\text{T})\sin\Big[\big(4.0\times10^{15}\text{s}^{-1}\big)\Big(\text{t}-\frac{\text{x}}{\text{c}}\Big)\Big]$ Find the maximum electric field and the average energy density corresponding to the electric field.
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Answer

$\text{B}=(200\mu\text{T})\sin\Big[\big(4.0\times10^{15}\text{s}^{-1}\big)\Big(\text{t}-\frac{\text{x}}{\text{c}}\Big)\Big]$$\text{B}_0=200\mu\text{T}$
$\text{E}_0=\text{C}\times\text{B}_0$
$\text{E}_0=200\times10^{-6}\times3\times10^{8}$
$\text{E}_0=6\times10^4$
Average energy density $=\frac{1}{2\mu_0}\text{B}_0^2=\frac{\big(200\times10^{-6}\big)^2}{2\times4\pi\times10^{-7}}$
$=\frac{4\times10^{-8}}{8\pi\times10^{-7}}=\frac{1}{20\pi}=0.0159=0.016$

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