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## 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

4 Replies Last Post 2010年9月18日 GMT+8 上午8:23

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.

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

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.