JEE Main · 2022 · 24 Jun 2022 · Shift 1 · EM Waves

In a material medium the ratio of the electric field to the magnetic field intensity of a plane wave is fixed by the intrinsic impedance of that medium, $\eta =\sqrt{\mu /\epsilon }=\sqrt{{\mu }_0/{\epsilon }_0}\sqrt{{\mu }_r/{\epsilon }_r}$, where $\sqrt{{\mu }_0/{\epsilon }_0}={\mu }_{0}c=4\pi \times 10^{-7}\times 3\times 10^8=120\pi \approx 377\Omega$ is the impedance of free space. With ${\mu }_r=1.61$ and ${\epsilon }_r=6.44$ the ratio under the root is ${\mu }_r/{\epsilon }_r=1.61/6.44=0.25$, so $\sqrt{{\mu }_r/{\epsilon }_r}=0.5$ and $\eta \approx 377\times 0.5\approx 188.5\Omega$. The electric field then follows from $E=\eta H$, since it is the magnetic intensity $H=4.5\times 10^{-2}\mathrm{A}{\mathrm{m}}^{-1}$ that is given here, not the magnetic flux density, so $E=188.5\times 4.5\times 10^{-2}\approx 8.48\mathrm{V}{\mathrm{m}}^{-1}$.