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Actually my problem is with the direction of both. I use CST to simulate a patch antenna. I guess that current density is the classic vector field \$ \mathbf{J} \$ (A/m^2) and actually follows the direction of the E-field. In my case, the patch antenna is placed on the yz plane. The current density direction according to the simulation is towards x-direction. On the other hand, the surface current has a completely different direction, actually towards y-direction. Practically, it follows the direction of the input transmission line of the patch antenna. Can you explain to me why they have a completely different direction?

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  • \$\begingroup\$ physics.stackexchange.com/questions/156251/… \$\endgroup\$ Commented Mar 13, 2021 at 19:36
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    \$\begingroup\$ That SE-Physics question is about current I (A) and so it is not relevant. The current density J (A/m^2) and the surface current density S (A/m) are both vectors. The direction of the surface current density is restricted to the plane of the surface. I do not know about the geometry the OP is concerned with, but is is easy to think of cases where they are perpendicular. For example, the surface current S might be due to an incident EM wave and be aligned with the polarization, while J might be due to applied potentials and be in any direction. \$\endgroup\$
    – 10ppb
    Commented Mar 13, 2021 at 20:35

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Surface currents and current densities are caused by different effects, so they can be different. Here are some notes:

Current density at DC aligns with electric fields, but at higher frequencies it gets more complicated since time and spatially varying magnetic field also affects current density.

Surface currents are caused by discontinuities in the magnetic field between interfaces (see https://en.m.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields).

That said, it's not obvious to me why they would point in different directions, just that it's possible they do since they are caused by different (and complicated) interactions between electric and magnetic fields inside and outside of the antenna.

Adding to that, patch antennas are "weird" in that the dipole or loop is not obvious because there's typically a grounded plane behind them with equal and opposite current, essentially cancelling out the magnetic field and making electric fields confined to the dielectric between the antenna and ground plane. The trick is that the edges have fringing fields that extend out into space that radiate (see https://www.antenna-theory.com/m/antennas/patches/antenna.php). Which, as a receiver, are the fields that couple to the antenna.

So I'm not totally sure of why it would happen in your case, but that there are reasons why it could happen.

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  • \$\begingroup\$ I thought the answer was obvious and I was missing something out. You helped me realize that the issue is quite complex, so I will try to take a deeper dive into some antenna theory books. Thank you. This analysis of mine began because I want to understand how to correlate the E-field components of the far-field zone of a patch antenna to the current direction, so I can better understand the resulting polarization, which is almost linear for a rectangular patch. \$\endgroup\$
    – bigboss
    Commented Mar 14, 2021 at 9:23

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