Permittivity of the Medium

We have just discussed the permittivity of the vacuum,

Now we will proceed with our discussion for the equivalent case in the medium.

In a medium (i.e. some kind of material), the value of k is smaller than its value in air or vacuum. In a medium, it is conventional to take

,

where $\epsilon$ is called the Permittivity of the medium and has the same dimensions as the permittivity of the vacuum, C²/N·m².

Definition:

Dielectric constant, $\kappa$, of a medium: \[ \rm \mathbf{\kappa = \frac{\varepsilon}{\varepsilon_{0}} = \frac{k_{0}}{k}} \]

Obviously, the Coulomb force is smaller in the medium by a factor $\kappa$ as compared to the vacuum value. (k is a Greek letter and pronounced "kappa".) For all materials, we have

Let's look at some typical value for the dielectric constant:

You can see that typical values for solids are between 1 and 10, and for liquids between 10 and 100. But for certain substances, we can also reach values of $\kappa$ up to 1000 or even 10000.

Warning:

Unfortunately the literature is full of conflicting definitions for the dielectric constant. Some books use the symbol $\epsilon$_r instead of $\kappa$. Even worse: some books use $\epsilon$ (without a subscript) instead of $\kappa$. For them $\epsilon$ is a dimensionless number, whereas in our case it has the dimensions C²/N$\cdot$ m². There is no way for you to avoid the confusion other than to come back to the definitions of $\epsilon$₀, $\epsilon$, and $\kappa$. So you should refer back to the top of this present page in case that you are confused.

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