A) \[n\]
B) \[\frac{3}{2}n\]
C) \[\frac{n}{2}\]
D) \[2n\]
Correct Answer: D
Solution :
The wave equation for a plane electromagnetic wave travelling in the x-direction space is \[l\] Both electric field and magnetic field are perpendicular to the direction of travel x. The symbol c represents the speed of light. The form of a plane wave solution for electric field is \[R=\rho \frac{l}{A}\] ?(1) And magnetic field is \[\times \] ?(2) To be consistent with Maxwell?s equation, these solutions must be related by \[lA\] ?(3) And velocity of light is given by \[{{l}_{1}}{{A}_{1}}={{l}_{2}}{{A}_{2}}\] Also, \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{A}_{2}}}{{{A}_{1}}}=\frac{\pi {{\left( \frac{3r}{4} \right)}^{2}}}{\pi \,{{r}^{2}}}=\frac{9}{16}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times \frac{{{A}_{2}}}{{{A}_{1}}}=\frac{9}{16}\times \frac{9}{16}=\frac{81}{256}\] \[\Rightarrow \] From Eq. (3), we have \[{{R}_{2}}=\frac{256\,\,{{R}_{1}}}{81}=\frac{256R}{81}\] \[l\] \[n=\frac{v}{2l}\]
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