Question

An electromagnetic wave is propagating in the positive x direction. At a given moment in time, the magnetic field at the origin points in the positive y direction. In what direction does the electric field at the origin point at that same moment? (Figure 1) Positive>x Negative x Positive y Negative y Positive z Negative z

Answer 1

The electric field of the electromagnetic wave at the origin point at that same moment must be along negative z direction in order for all the given conditions to be true. Thus, the last option is correct.

It is given to us that -

The electromagnetic wave is propagating in the positive x direction

At a given moment in time, the magnetic field at the origin points in the positive y direction

We have to find out the direction in which the electric field at the origin is pointing at that same moment.

We know that in an electromagnetic wave propagation, electric and magnetic field components are perpendicular to each other, and wave propagation is perpendicular to both wave components.

This concept is followed by the condition that the velocity is perpendicular to both the electric and magnetic fields.

So, this theory can be represented as -

$v^{- > } = E^{- > } * B^{- > }$

where,

$v^{- > }$ = velocity

$E^{- > }$ = Electric field

$B^{- > }$ = Magnetic field

It is known to us that the electromagnetic wave is propagating in the positive x direction.

]This implies that the velocity, $v^{- > }$ is towards positive x direction.

Also, it is given to us that the magnetic field at the origin points in the positive y direction.

This implies that the magnetic field, $B^{- > }$ is in the positive y direction.

So, to prove that the given conditions are true, the electric field of the electromagnetic wave at the origin point at that same moment must be along negative z direction. Thus, the last option is correct.

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