# Relating electric constants to the speed of light ?

• cragar
In summary, Maxwell's discovery of the relationship between the vacuum permeability and permittivity constants and the speed of light ultimately led to the development of special relativity. This was achieved through the addition of displacement current to his equations, which allowed for the prediction of electromagnetic waves traveling at the speed of light.
cragar
1/sqrt(EP)=c
where E= Permittivity constant
P= permeability constant .
and how it would lead to problems and eventually lead to relativity
can some one give me a hint what he is getting at this is not a home work problem he just wanted us to think about it .

Well... hopefully you know that the vacuum permeability and permittivity (the electric and magnetic constants) were determined by experiments which, at the time, seemed to be completely unrelated to light. I'm talking about measuring the tiny forces between charged pith balls and electric wires with current flowing through them, that sort of thing. Then they calculated $1/\sqrt{\epsilon_0 \mu_0}$ and found that it was equal to the speed of light.

Now think about this: what if you took all those experiments on some futuristic spaceship, fired it up to half the speed of light, and did the experiments again? What would happen to the value of the electric and magnetic constants?

thanks for the response , so like if I have charged particles and I am moving
to someone on the ground the particles are moving so we would perceive different magnetic fields .

Maxwell's addition of the displacement current that completed his equations also allowed him to derive wave equations for the electric and magnetic fields. The speed of these wave equations were found to be c. So Maxwell's equations not only predict electromagnetic waves, they also stipulate that their speed in vacuum is c.

This is the starting point for deriving special relativity.

## 1. What is the relationship between electric constants and the speed of light?

The electric constant, also known as the permittivity of free space, is a fundamental constant in physics that determines the strength of the electric force between two charged particles. It is directly related to the speed of light in a vacuum, as it appears in the equation c = 1/√(μ₀ε₀), where c is the speed of light, μ₀ is the permeability of free space, and ε₀ is the electric constant. This means that the speed of light is inversely proportional to the square root of the product of these two constants.

## 2. How do electric constants affect the propagation of light?

Electric constants play a crucial role in determining the speed at which light travels through a medium. In a vacuum, where ε₀ = μ₀ = 1, the speed of light is at its maximum value of approximately 299,792,458 meters per second. However, in a medium such as air or glass, the speed of light is slower due to the presence of electric and magnetic fields, which are influenced by the permittivity and permeability of the medium.

## 3. Can electric constants be measured experimentally?

Yes, the electric constant can be measured experimentally using various techniques such as capacitance and electromagnetic resonance methods. These experiments involve measuring the electric field and its interactions with other charged particles to determine the value of ε₀. The current accepted value for the electric constant is approximately 8.854 x 10^-12 farads per meter.

## 4. Are there any other physical phenomena that are affected by electric constants?

Besides the speed of light, electric constants also play a role in determining the strength of electromagnetic interactions between charged particles, the behavior of electric fields in conductors and insulators, and the properties of capacitors and other electrical components. They are also essential in the study of quantum electrodynamics, which explains the interaction between light and matter on a subatomic level.

## 5. How have our understanding and measurement of electric constants evolved over time?

The concept of electric constants has evolved significantly over time, starting with the work of scientists such as Michael Faraday and James Clerk Maxwell in the 19th century. Their experiments and theories laid the foundation for our current understanding of electric constants and their relationship to the speed of light. The measurement of these constants has also become more precise over time, with advancements in technology and experimental techniques allowing for more accurate values to be determined.

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