# Assumptions made when deriving the speed of light

• Parker Mays
In summary, the problem the author is experiencing is that they need to make two assumptions in order to derive the speed of light- one being that there are no net charge or displacement currents in space, and the other being that the medium is mathematical and does not have any physical properties (like charge or displacement current). Once they make these assumptions, they can derive that the speed of light is equal to 1/√(εμ) or ≅ 3E8 meters per second.

## Homework Statement

The problem I have been working with recently has been deriving the speed of light using maxwells equations, however in order to do this I must make two assumptions; there is no net charge or displacement currents in the space in which I am attemptin to derive the speed of light. If I make these assumptions I am able to find that the speed of light is equal to 1/√(εμ) or ≅ 3E8 meters per second. I do not understand why I must make these assumptions.

## Homework Equations

Maxwell's Equaitons

Every physical theory must have some assumptions that pin the theory to the real world.

My feeling is that it is reasonable to say that there is no net charge or displacement currents in space, since space is considered empty (in an idealized sense) and without any charge present there can be no displacement currents.

However, in Maxwell's time, these assumptions were much harder to accept since there was an understanding that waves traveled through a medium and that the medium being physical might have these properties of charge and displacement current. Now of course we know that space is empty.

In making these assumptions (a special case to test), we discover waves whose speed matches that of light and then make the jump to light being an electromagnetic phenomena.

Here's a discussion of the derivation that explains some of the reasoning:

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Maxwell_Eq.html

While searching on this question, I ran into this presentation of Maxwell's equations that you might find interesting:

https://web.ewu.edu/groups/technology/Claudio/ee209/f09/Lectures/physics.pdf

Last edited:
• Buzz Bloom
Parker Mays said:

## Homework Statement

The problem I have been working with recently has been deriving the speed of light using maxwells equations, however in order to do this I must make two assumptions; there is no net charge or displacement currents in the space in which I am attemptin to derive the speed of light. If I make these assumptions I am able to find that the speed of light is equal to 1/√(εμ) or ≅ 3E8 meters per second. I do not understand why I must make these assumptions.

## Homework Equations

Maxwell's Equaitons
Because if you don't make those assumptions then the Maxwell equations would not lead to the wave equation. For example, ∇⋅E would not be zero and so ∇2E would not = εμ ∂2E/∂t2, the wave equation for E.

P.S. I think you meant to say "conduction currents", not "displacement currents". Without the latter there would be no ∂E/∂t and no waves.

Okay this makes a lot more sense now, thank you for your explanations.