For a plane electromagnetic wave propagating in -direction, which one of the following combinations gives the correct possible directions for electric field and magnetic field respectively? [2021]

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Q.
For a plane electromagnetic wave propagating in $x$ -direction, which one of the following combinations gives the correct possible directions for electric field $(E)$ and magnetic field $(B)$ respectively [2021]

1 $- \hat{j} + \hat{k}, - \hat{j} + \hat{k}$

2 $\hat{j} + \hat{k}, \hat{j} + \hat{k}$

3 $- \hat{j} + \hat{k}, - \hat{j} - \hat{k}$

4 $\hat{j} + \hat{k}, - \hat{j} - \hat{k}$

Ans.
(3)

As $\vec{E}$ and $\vec{B}$ are perpendicular to each other, their dot product must be zero.

$\vec{E} \cdot \vec{B} = 0$

Also, the wave is propagating along x-axis i.e. cross product of $\vec{E} \times \vec{B}$ is along $\hat{i} .$

Out of given options, only $(- \hat{j} + \hat{k}),$ $(- \hat{j} - \hat{k})$ follow the above conditions.

Solution

Q.
For a plane electromagnetic wave propagating in $x$ -direction, which one of the following combinations gives the correct possible directions for electric field $(E)$ and magnetic field $(B)$ respectively [2021]

1 $- \hat{j} + \hat{k}, - \hat{j} + \hat{k}$

2 $\hat{j} + \hat{k}, \hat{j} + \hat{k}$

3 $- \hat{j} + \hat{k}, - \hat{j} - \hat{k}$

4 $\hat{j} + \hat{k}, - \hat{j} - \hat{k}$

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Solution

Q. For a plane electromagnetic wave propagating in x-direction, which one of the following combinations gives the correct possible directions for electric field (E) and magnetic field (B) respectively [2021]

1 -j^+k^, -j^+k^

2 j^+k^, j^+k^

3 -j^+k^, -j^-k^

4 j^+k^, -j^-k^

Ans. (3) As E→ and B→ are perpendicular to each other, their dot product must be zero. E→·B→=0 Also, the wave is propagating along x-axis i.e. cross product of E→×B→ is along i^. Out of given options, only (-j^+k^),(-j^-k^) follow the above conditions.

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Q.
For a plane electromagnetic wave propagating in $x$ -direction, which one of the following combinations gives the correct possible directions for electric field $(E)$ and magnetic field $(B)$ respectively [2021]

1 $- \hat{j} + \hat{k}, - \hat{j} + \hat{k}$

2 $\hat{j} + \hat{k}, \hat{j} + \hat{k}$

3 $- \hat{j} + \hat{k}, - \hat{j} - \hat{k}$

4 $\hat{j} + \hat{k}, - \hat{j} - \hat{k}$