Question

Lightwave is traveling along the $y$-direction. If the corresponding $\overrightarrow{E}$ vector at any time along the $x$−axis, the direction of $\overrightarrow{B}$ vector at that time is along

• A. $x$−axis
• B. $y$−axis
• C. $-z$−axis
• D. $z$−axis

Answer 1

The correct option is C

$-z$−axis

1. We know the direction of propagation, $\overrightarrow{v}=\overrightarrow{E}\times \overrightarrow{B}$, Where $\overrightarrow{E}=$Electric field, $\overrightarrow{B}=$Magnetic field, $\overrightarrow{v}=$Direction of propagation.
2. And $\overrightarrow{E,}\overrightarrow{B},\overrightarrow{v}$ all are perpendicular to each other.
3. Also, we know by Maxwell's law, $\overrightarrow{v}=\overrightarrow{E}\times \overrightarrow{B}$, So now $\overrightarrow{y}=\overrightarrow{x}\times \overrightarrow{B}$ (Given data)
4. Now if $\overrightarrow{x}\times \overrightarrow{z}=-\overrightarrow{y}$ and if $\overrightarrow{x}\times \left(-\overrightarrow{z}\right)=\overrightarrow{y}$
5. Thus, if light is travelling in positive y-direction and electric field along x-axis,then $\overrightarrow{B}$ must be in -z direction.
6. Lightwave is an electromagnetic wave in which $\overrightarrow{E}$ and $\overrightarrow{B}$ are making right angles to each other.
7. Also, they are at right angles to the direction of wave propagation.
8. For electromagnetic waves, $\overrightarrow{E}$ and $\overrightarrow{B}$ are always perpendicular to each other and perpendicular to the direction of propagation.
9. Hence, there will be only one direction in which $\overrightarrow{B}$ can go. i.e +z-axis
10. So from the given information in the question, the direction of the $\overrightarrow{B}$ is in the positive z-direction.
11. If wave direction is towards negative y-axis, then $\overrightarrow{B}$ will be in the positive z-axis.

Hence, the correct options are options C.