Dielectric Boundary Condition Question

[Apteronotus]

Hi,

I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this.

Suppose we have a dielectric in space subjected to some external static electric field.

I have read (without explanation) that at the boundary of the dielectric the potential \Phi satisfies

<br /> k\frac{\partial \Phi}{\partial n_i} = \frac{\partial \Phi}{\partial n_e} <br />

where \frac{\partial}{\partial n} represent the derivatives along the outward unit normal just interior, i, and just exterior, e, of the dielectric and k is the dielectric constant.

can anyone shed some light on why this is so?

 

[MisterX]

The equation relates the normal component of the electric fields on either side of the boundary
<br /> \frac{\partial \Phi}{\partial x} = -E_x<br />

The boundary condition is

\epsilon_1 E^\perp_1 - \epsilon_2 E^\perp_1 = \sigma_q

where \sigma_q is the charge density on the surface.

This can be shown by using Gauss's law with a "pillbox" surface.

http://www.scribd.com/doc/136393324/27/Boundary-conditions-for-perpendicular-field-components

This corresponds to your equation when \frac{\epsilon_i}{\epsilon_e} = k and \sigma_q = 0

 

[Apteronotus]

MisterX you are amazing!
I am grateful. Thank you.