Question

What is the exact relation between Polarization (Dipole moment per unit volume) and the External electric field?

Answer 1

This it the given relation between P and E.
But I read everywhere else that the susceptibility is a dimensionless number.
So for that to work, equation 2.37 must have an epsilon zero on the right hand side.
Can someone explain to me what is going on? And also how to derive the expression between the susceptibility and dielectric constant (relative permittivity) in easiest way possible.. As simple case as you can.. only for linear isotropic dielectrics!

Answer 2

I derived it this way.. can someone check this?

Answer 3

You are right, \(\vec P=\chi \epsilon_o\vec E\) and \(\chi\) is dimensionless.

This holds for an isotropic medium.

If not, \(\chi\) is a 3x3 matrix.

Answer 4

So the snapshot in the textbook is wrong ... correct?

And the derivation I posted? Is that accurate?

Answer 5

I cannot open the snapshot. Can you post it again, please?
Your derivation seems ok.

Answer 6

In general the relationship between the dipole moment P gained by an object located within an external field E_0, is given by the subsequent relationship:
\[{\mathbf{P}} = {\chi _e}{\mathbf{E}}\]
where \chi_e is the electric susceptibility, E is the total field inside the polarized matter, so the external field E_0 is a function of E

Answer 7

for example in the case of a uniformly polarized sphere, we can write the subsequent relationship, between the external field E_0 and the gained dipole moment P per unit of volume (or polarization) by that sphere:
\[\Large {\mathbf{P}} = \frac{3}{{4\pi }}\left( {\frac{{\varepsilon - 1}}{{\varepsilon + 2}}} \right){{\mathbf{E}}_{\mathbf{0}}},\quad ({\text{CGS system}})\]
where \epsilon is the dielecytric constant of the sphere

Answer 8

Okay I will re post it

@michele_laino
according to that, khi will have some dimensions..
the relation given almost everywhere including Feyman lectures is

\[P = \epsilon_o \chi_E E\]

Answer 9

Let's consider a dielectric slab into an external electric field:

Answer 10

in doing that, the dielectric slab will polarize itself so an internal electric field will appear inside that dielectric slab:

where P is the polarization vector, and E_1 is the induced electric field inside the slab