Question about the "Reciprocity"

[TWang]

Hi everyone:
There is somthing i don't understand in the book "Time-Harmonic Electromagnetic Fields" by R.F. Harrington. Can anyone answer my question?

In the end of the chapter 3-8,the Reciprocity part, the author want to tell us that an electric current impressed along the surface of a PEC radiate no field. This confuses me because when we're studying dipole antenna, it is the current on the dipole that radiates, right?

The author adds a statement in the last paragraph, which i don't know its meaning either. "We can think of Ia (current impressed along the PEC surface i suppose) as inducing currents on the conductor such that these currents produce a free-space field equal and opposite to the free-space field of Ia"

Thank you for your kindly response.

 

[rautio]

Hi TWang -- I was a student of Roger Harrington. I had the same question you did. He explained it to me. A current flowing in a conductor is not impressed in the conductor.

Imagine a current flowing a short distance above a conductor. You can take the conductor away and substitute an image current flowing an equal distance below the conductor. The image current is flowing in the opposite direction.

Now make the separation between the current and the image smaller and smaller. Because they are flowing in opposite directions, the total field get less and less. Each current cancels out the other more and more. If you take it to the limit, where the separation goes arbitrarily close to zero (but never actually equals zero), then the fields go arbitrarily close to zero. This is a current impressed on a PEC.

A current flowing in a PEC does not have an image to cancel its fields. Thus, your dipole antenna, with current flowing in the conductor, works just fine. But if you move your dipole arbitrarily close to a PEC plane, it will no longer radiate anything, because it is too close to its image. Its image has current flowing in the opposite direction and cancels out all fields.

 

[TWang]

Hi rautio:

Thank you for giving me such a good explanation. Now I know what it means by the current on a PEC doesn't radiate. Bravo !