Waiting
Login processing...

Trial ends in Request Full Access Tell Your Colleague About Jove

33.5: Propagation Speed of Electromagnetic Waves
TABLE OF
CONTENTS

JoVE Core
Physics

A subscription to JoVE is required to view this content.
You will only be able to see the first 20 seconds.

Education
Propagation Speed of Electromagnetic Waves
 
TRANSCRIPT

33.5: Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:

Equation1

Figure1

Consider a plane wavefront traveling in the positive x-direction as shown in figure. Over it, consider a rectangle in the xz-plane, with an area vector in the positive y-direction. The integration is performed counterclockwise around the rectangle to solve the left-hand side of Ampere's law. The magnetic field is either zero or perpendicular to the length elements except for one length, where the field is parallel. This length contributes to the integral, giving a non-zero value.

To satisfy Ampere's law, the right side of Ampere's law must also be non-zero. Therefore, the electric field must have a y-component that can provide a non-zero time derivative of electric flux. It also establishes that the electric and magnetic fields must be mutually perpendicular. The electric flux increases to a positive value in time, dt. The rate of change of electric flux can be substituted in Ampere's law.

Equation2

Since electromagnetic waves are consistent with all of Maxwell's equations, the obtained expression is compared with the expression derived using Faraday's law, which gives wave propagation speed in the vacuum.

Equation3

When the numerical values of permeability and permittivity are substituted, the propagation speed obtained is equal to the speed of light.

Equation4

It implies that the assumed wave is consistent with all of Maxwell's equations, provided that the wavefront moves with speed given above, which is recognized as the speed of light. Note that the exact value of the speed of light is defined to be 299,792,458 m/s. 


Suggested Reading

Get cutting-edge science videos from JoVE sent straight to your inbox every month.

Waiting X
Simple Hit Counter