Q154 / 160 · AP EAMCET 2023 (18 May Shift 1) · Physics

If $\mathrm{E}_{\mathrm{O}}$ and $\mathrm{B}_{\mathrm{o}}$ are the magnitudes of the electric and magnetic fields respectively of an electromagnetic wave in vacuum, then among the following the correct relation is ( $\mu_0-$ permeability of free space, $\varepsilon_0-$ permittivity of free space)

  • A
    $E_o=B_o \sqrt{\mu_o \varepsilon_o}$
  • B
    $\mathrm{E}_{\mathrm{o}} \varepsilon_{\mathrm{o}}=\mathrm{B}_{\mathrm{o}} \mu_{\mathrm{o}}$
  • Correct answer
    C
    $\mathrm{E}_{\mathrm{o}} \sqrt{\varepsilon_{\mathrm{o}}}=\frac{\mathrm{B}_{\mathrm{o}}}{\sqrt{\mu_{\mathrm{o}}}}$
  • D
    $\frac{\mathrm{E}_{\mathrm{o}}}{\sqrt{\varepsilon_{\mathrm{o}}}}=\frac{\mathrm{B}_{\mathrm{o}}}{\sqrt{\mu_{\mathrm{o}}}}$

Solution

Speed of light is given as: $\begin{gathered}E_o=c B_o \\ c=\frac{E_o}{B_o}\end{gathered}$ According to maxwell speed of light is given as $\begin{aligned} & c=\frac{1}{\sqrt{\mu_0 \epsilon_0}} \\ & \therefore \frac{E_o}{B_o}=\frac{1}{\sqrt{\mu_o \epsilon_0}} \\ & E_o \sqrt{\epsilon_0}=\frac{B_o}{\sqrt{\mu_o}}\end{aligned}$

Hence, the correct answer is option: 'C'.

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