Question

A plane electromagnetic wave traveling in the positive direction of an x axis in vacuum has components Ex =Ey =0 and Ez =(2V/m)cos(3.14∗10^−15s^−1(t− x/c)). (a) What is the amplitude of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate? (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 1

The general equation of a wave is given by,

Given,

Therefore,

a) Electromagnetic waves travel with the velocity of light and is given by,

b) Given, the plane electromagnetic wave is traveling in the positive direction of  X-axis and the electric field is oscillating in the Z-axis with components

Hence according to the velocity of the electromagnetic wave,

(cross product)

Magnetic field oscillates in the Y-axis. (Ans.)

ie, All the three are mutually perpendicular to each other.

c) The direction of propagation of the electromagnetic wave is given by the equation

(cross product)

So if the direction of the propagation is to +X-axis, and the direction of the electric field is +Z-axis. Substituting in the above equation,

where is in the direction of negative Y axis     (Ans.)