Question

A radio wave is traveling in the negative$\mathrm{y}$-direction. What is the direction of $\overrightarrow{\mathrm{E}}$at a point where$\overrightarrow{\mathrm{B}}$is in the positive$\mathrm{x}$-direction?

Short answer

Direction of $\overrightarrow{\mathrm{E}}$is in negative$\hat{\mathrm{z}}$direction.

Step-by-step solution

The travelling direction of electromagnetic waves is depicted in this diagram.

Figure is,

Explanation

The vector of Poynting,

$\overrightarrow{\mathrm{S}}=\frac{1}{{\mathrm{\mu }}_{\mathrm{o}}}\overrightarrow{\mathrm{E}}\times \overrightarrow{\mathrm{B}}$

The EM wave's path is indicated by this arrow.

$\overrightarrow{\mathrm{B}}$is in $\hat{\mathrm{x}}$direction.

$\overrightarrow{\mathrm{E}}$should be included inlocalid="1648791112140">-z^direction.

So,

$\mathrm{E}\times \overrightarrow{\mathrm{B}}$is in direction$-\hat{\mathrm{y}}$.

localid="1648791725580" $\overrightarrow{\mathrm{E}}$paints inlocalid="1648791733560" $-\hat{\mathrm{z}}$direction (negative localid="1648791738614" $\mathrm{z}-$direction.)