Local field at an atom

**manofphysics** · Nov29-09, 06:32 AM

I just have a small question regarding lorentz cavity:

Refer to a small lorentz cavity in a uniformly polarised dielectric. as shown in fig.
$LaTeX Code: E_{ex}$ : External electric field.
$LaTeX Code: E_{P}$ : electric field in the uniformly polarised dielectric (when sphere has NOT been cut out)
$LaTeX Code: E_{L}$ :Electric field due to surface charge on cavity
$LaTeX Code: E_{near}$ :Field due to dipoles inside cavity.

Now, $LaTeX Code: E=E_{ex}+E_{P}+E_{L}+E_{near}$

But, does not $LaTeX Code: E_{P}$ change if we cut out a sphere from the polarised dielectric?
Is it that we are neglecting the small change in $LaTeX Code: E_{P}$ due to cut out sphere and our result is an useful approximation, but not exact?

Please, any help will be appreciated. I need to understand this for my term exam.

**alxm** · Dec1-09, 03:19 AM

I'm not sure, but offhand: If you form the cavity adiabatically, then E_L would compensate for the change in E_P, wouldn't it? So I suspect that's the approximation involved.