Question

A plane electromagnetic wave traveling in the positive direction of an x axis in vacuum has components Ex = Ey = 0 and Ez = (3.1 V/m) cos[(? × 1015 s-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? Assume that the speed of light is 2.998*108 m/s.

Answer 1

E_x = E_y = 0

E_z = (3.1 V/m) cos[(?*10¹⁵ s^-1)(t - x/c)]

here , maximum electric field E_m = 3.1 V/m

a)

the amplitude of the magnetic field is

                B_m = E_m/c

                      = (3.1 V/m) / ( 2.998*10⁸ m/s)

                      = 1.034*10^-8 T

b)

the waves oscillates in z-direction and its travels in +ve x-direction.

so , B_x = B_z = 0

therefore , the oscillation of the magnetic field is parallel to the y-axis.

c)

electromagnetic wave propagation is determined by E*B.

if the electric field component is in the positive direction of the z axis ,

then the magnetic field is in the y-axis (direction)

     B_y = B_m cos[(?*10¹⁵ s^-1)(t - x/c)]

           = (1.034*10^-8 T) cos[(?*10¹⁵ s^-1)(t - x/c)]