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An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\varepsilon_r=9$, has the electric field, $E_x=E_0\sin(kz-2\pi\times10^6t)$ Vm$^{-1}$ where $E_0$ is the amplitude and k is the wave vector. Among the following options, the incorrect choice is
Detailed Solution
(1) $v=\frac{c}{\sqrt{\mu_r\varepsilon_r}}=\frac{3\times10^8}{\sqrt{1\times9}}=10^8$ m/s - correct. (2) $\omega=2\pi f=2\pi\times10^6 \Rightarrow f=10^6$ Hz, so $\lambda=\frac{v}{f}=\frac{10^8}{10^6}=100$ m, not 300 m - incorrect. (3) $\frac{E_0}{B_0}=v \Rightarrow B_0=\frac{E_0}{v}$, so the correct relation is $B_y=\frac{E_0}{v}\sin(kz-2\pi\times10^6t)$; as printed with $B_0/v$ it is also incorrect. (4) The wave propagates along +z - correct. ALLEN's key accepts both (2) and (3); the answer used here is (2).