For plane electromagnetic waves propagating in the positive Z - direction. The combination which gives the…

For plane electromagnetic waves propagating in the positive Z - direction. The combination which gives the correct possible direction for $\bar{E}$ and $\bar{B}$ fields respectively is
  1. $(-2 i-3 j)$ and $(3 i-2 j)$
  2. $(3 i+4 j)$ and $(4 i-3 j)$
  3. $(i-2 j)$ and $(-2 i-j)$
  4. $(-2 i+3 j)$ and $(i+2 j)$

Solution

As, $\overrightarrow{\mathrm{E}} \perp \overrightarrow{\mathrm{B}} \Rightarrow \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{B}}=0$ $\begin{aligned} & \text { For } \overrightarrow{\mathrm{E}}=(-2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}), \overrightarrow{\mathrm{B}}=(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}) \\ & \therefore \quad \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{B}}=(-2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}) \cdot(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}) \\ & =(-2)(3)+(-3)(-2)=-6+6=0\end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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