Chapter 33, Problem 1Q

To determine

To find:

a) The direction of the wave travel.

b) The direction of oscillation of the electric field.

Answer to Problem 1Q

Solution:

a) The direction of wave travel is along the positive direction of the z axis.

b) The direction of oscillation of electric field is along x axis.

Explanation of Solution

1) Concept:

Analyzing the given equation, we can find the direction of the electromagnetic wave and the direction of the electric field component.

2) Given:

The equation of the magnetic field oscillating parallel to y axis is

$B_y=B_m\mathrm{ }\sin (kz-\omega t)$

3) Calculations:

a) From the given equation, the term ‘kz’ denotes that the wave is travelling along z direction. And the sign indicates that the wave is travelling along the positive z axis.

b) As the magnetic field is oscillating parallel to y axis and the wave is traveling along z direction. The electric field must oscillate parallel to x-axis, perpendicular to both, the direction of the propagation of wave and the magnetic field.

Conclusion:

Using the information of the given equation, we can indicate the direction of the wave and its electric and the magnetic field components.