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Physics · 2023 · 2 marks
CBSE 2023 · Region 1 · Set 2 · Q22
A plane electromagnetic wave propagates in vacuum along x -axis. (a) Give the direction of electric field and magnetic field vectors. (b) E_0 and B_0…
A plane electromagnetic wave propagates in vacuum along x -axis.
(a)
Give the direction of electric field and magnetic field vectors.
(b)
$\displaystyle \mathrm{E}_{0}$ and $\displaystyle \mathrm{B}_{0}$ are the magnitudes of electric and magnetic fields respectively in a plane electromagnetic wave. Find the ratio of energy densities of electric field and magnetic field.
Marking-scheme solution
(a)
Mentioning direction of electric field and magnetic field vectors $\displaystyle 1$
(a)
Electric field vector and magnetic field vector are along y-axis and z-axis or vice versa.
(b)
\(\displaystyle \mathrm{u}_{\mathrm{E}}=\frac{1}{2} \varepsilon_{o} \mathrm{E}^{2}{ }_{o} \quad \mathrm{u}_{\mathrm{B}}=\frac{1}{2} \frac{\mathrm{B}^{2}{ }_{o}}{\mu_{o}}\)
\(\displaystyle \frac{\mathrm{u}_{\mathrm{E}}}{\mathrm{u}_{\mathrm{B}}}=\mu_{o} \varepsilon_{o} \frac{\mathrm{E}_{o}{ }^{2}}{\mathrm{B}_{o}{ }^{2}}\)
Using \(\displaystyle \frac{\mathrm{E}_{o}}{\mathrm{B}_{o}}=\mathrm{c}\) and \(\displaystyle \mathrm{c}=\frac{1}{\sqrt{\mu_{o} \epsilon_{o}}}\)
\(\displaystyle \frac{\mathrm{u}_{\mathrm{E}}}{\mathrm{u}_{\mathrm{B}}}=\mu_{o} \varepsilon_{o} \mathrm{c}^{2}=1\)
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