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## 3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

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You Zhe Ho

September 15, 2010 4:15pm UTC

3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

Dear all
I'm a beginner at COMSOL 3.5a

IN 3D => RF model => Electromagnetics waves

how do I express "surface charge density "?

I know the expression of the surface charge density magnitude is "normJs_rfw"?

THANH YOU ,

BEST REGARDS

DANNY

Robert Koslover

September 15, 2010 8:37pm UTC in response to You Zhe Ho

Re: 3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

Short answer: Well, for a *conducting* surface in empty space, the surface charge density can be expressed as the norm of the electric field divided by epsilon_0. I.e., surface charge density [coulombs/m^2] = normE_rfw/epsilon0_rfw. This follows simply from Gauss' law of electrostatics (which is valid in the RF case as well). (Remember: "Del dot E = rho / epsilon_not" ) (Just consider a thin pillbox around the surface and the integral form of Gauss' law.)

More complicated example: For an interface between two dielectrics, you''ll probably want to begin with D instead of E, and derive an expression that is similar, but based on the more general expression, "Del dot D = rho free" and also recognize the existence of electric displacement fields on *both* sides of the interface. For example, suppose your interface is the x-y plane, so that the normal points along the z axis. Then the free surface charge density on the interface should be given by Dz_rfw (on the right side) - Dz_rfw (on the left side). Note the discontinuity of the field, which I suppose may complicate this. Regardless, I suppose you could find the surface charge at a dielectric interface by interrogating your computed D-field results near the boundary on both sides, in post processing inspection. And then, of course, there is the "bound" charge density to consider also in the case of dielectrics. You might want to re-check the exact EM definitions, when working with dielectrics. Good luck.

Robert Koslover

September 15, 2010 8:40pm UTC in response to You Zhe Ho

Re: 3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

Correction for the conducting surface case: Surface charge density = epsilon0_rfw*normE_rfw.

You Zhe Ho

September 17, 2010 5:23am UTC in response to Robert Koslover

Re: 3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

but "Surface charge density = epsilon0_rfw*normE_rfw" ,the normE_rfw means a scalar ,ie, normE_rfw is the magnitude of the electric field not a vector.

if the normE_rfw is normal to any surface ,then it could be right.

Robert Koslover

September 18, 2010 12:23am UTC in response to You Zhe Ho

Re: 3D => RF model => Electromagnetics waves how do I express the "surface charge density "?

Well, I'm not 100% sure what you mean here, but you sound confused about "norm" vs "normal." You are correct that normE_rfw is a scalar. It is the magnitude (or "norm") of E. Now, for a perfectly conducting surface, E will also be perpendicular to that surface. And any vector perpendicular to a surface is said to be "normal" to that surface. So the vector E will be normal to the conducting surface.

And finally, in the case of a dielectric junction, although E (and likewise D) may not be normal to the surface, the normal (aka, perpendicular to the surface component) of E (or D) is still what you would want to use when extracting surface charge densities.

Does that help?

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