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A plane electromagnetic wave traveling in the positive direction of an x axis in vacuum has components Ex= Ey = 0 and Ez = (2.0 V/m) cos[(π × 1015 s−1)(t − x/c)]. When the electric field component is in the positive direction of the z axis at a certain point P, what is the direction of the magnetic field component there?

Answer :

whitneytr12

Answer:

The direction of the magnetic field component will be in the negative direction of y.

Explanation:

The  propagate direction of the wave if given by the cross product between E and B.

Now, if the direction of the propagate wave is in the positive x axis (+x) and the direction of the electric field component is in the positive direction of the z axis. We will have:

[tex]\hat B=\hat z \times \hat x[/tex]

If we use the right hand rule we will have that the direction is -y.

Therefore the direction of the magnetic field component will be in the negative direction of y.

I hope it helps you!

The direction of the magnetic field component there is negative y - direction.

The given parameters:

Ex = Ey = 0

[tex]E_z = (2.0 \ V/m) \ cos[(\pi \times 10^{15} \ s^{-1})(t - x/c)][/tex]

The direction of the electromagnetic wave is in positive x-direction.

When the electric field component is in the positive direction of the z axis at a certain point P, the direction of the magnetic field component there is determined as follows.

Apply cross product of vectors;

[tex]i \times k = -j[/tex]

where;

  • i positive x-direction of the vector
  • k is the positive z-direction of the vector

[tex]E_i \times E_k = - E_j[/tex]

Thus, the direction of the magnetic field component there is negative y - direction.

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