# What's the nuance of susceptibility and permittivity?

I want to ask a question about the meaning of the names of some dielectric properties. I'm not a native English speaker, so I don't know why the name of the properties are susceptibility and permittivity. It could be trivial, but I want to understand why they are named this way.

As far as I understand, susceptibility is about how susceptible the material is. Atoms are susceptible to electric fields.

Then what about permittivity? Do they permit something? Permittivity is about total field and polarization ($\mathbf{D}= \epsilon_0 \mathbf{E} + \epsilon_0 \chi_e \mathbf{E}$ $=\epsilon_0 \mathbf{E}+\mathbf{P}$).

But to me, both look almost the same. Why don't you call susceptibility permittivity, and permittivity susceptibility?

It is indeed a bit confusing. Qualitatively (and only looking at the $$\vec E$$ field), the permittivity of a dielectric material is not the degree of permitting the $$\vec E$$ field to penetrate the material but the degree of resistance. That is, the greater the permittivity of a material, the more difficult it is for the $$\vec E$$ field to find its way into the material.

The susceptibility of a material is the degree of the receptiveness for the $$\vec E$$ field. The greater the receptiveness for a dielectric material, the more the $$\vec E$$ field can enter the material and the greater the polarization in the dielectric, opposing the applied field. In the process, the material acquires potential energy.

If there is no dielectric material at all (or any other material), i.e. in a vacuum, the susceptibility is zero (there is no dielectric to receive the $$\vec E$$ field): $$\chi =({\frac{\epsilon}{{\epsilon}_0}}-1)$$, where $$\chi$$ is the susceptibility, $$\epsilon$$ the absolute permittivity, and $${\epsilon}_0$$ the permittivity in vacuum (the ratio of these is called the relative permittivity $${\epsilon}_r$$ which is one for the vacuum, so the susceptibility $$\chi$$ is zero in vacuum). On the other hand, the vacuum has maximal resistance to let the $$\vec E$$ field go through, and the permittivity has it's minimum value $${\epsilon}_0=8,845*{10}^{10}(\frac F m)$$.

I agree that you could just as well interchange the terms "permittivity" and "susceptibility". They are in a sense each other's inverses.

And, of course, you can say that these terms are just names that are historically determined, but then you can give every physical concept just arbitrary names of which you just have to learn the definitions. It seems that the definitions of names that cover these definitions are much easier to learn. Why hold on to names that were invented a long time ago and which don't (entirely) cover the definitions? That's a very conservative point of view which can cause much confusion (as is clear by the question asked).

Frankly, I think you're reading too much into it. There are multiple related concepts and we need different names for them to be able to work effectively, so we give them related-but-different names and just work directly with the concept. The English words are not meant to capture the full nuance and meaning of the concept, it's the definitions that do that. The English names were chosen through a historical process, the details of which no longer matter much (and if that is your question, it's a matter for History of Science and Mathematics), and which are essentially irrelevant to the everyday use.

Simply put, learn and understand the definitions, and don't worry too much about just why some English word got chosen to hold the concept.