# Love's equivalence principle for a perfect electric conductor

1. Apr 10, 2012

### eliotsbowe

Hello, I'm having some issues with Love's equivalence principle.
I'm studying Balanis' "Antenna theory" (1997), here's a (legal) fragment of the section in question:

http://www.uniroma2.it/didattica/ap1/deposito/02_2-Balanis-Equivalence_Theorems.pdf

I'm trying to understand the following statement (page 331, figure 7-8 b):
"The electric current density Js, which is tangent to the surface S, is short-circuited by the electric conductor."

May someone explain the reason for Js to be considered short-circuited on the surface of the perfect electric conductor?

2. Apr 10, 2012

### sambristol

The tangential component tries to flow along the surface of the conductor so is 'short circuited' ie on a perfect conductor it generates no potential difference.

3. Apr 10, 2012

### eliotsbowe

What points should I pick to compute that potential difference? I mean, one is on the surface S, but what's the second one? Besides, why is that potential difference null?
Thanks

4. Apr 11, 2012

### sambristol

OK don’t get blocked by this, don't fear it. It is just a technique to solve a generalised situation in EM field theory.

So what you are trying to do is to model the far field radiation of a complicated system of currents and EM fields by replacing them with a simpler system which gives the same radiation far from the source.

The integrals involved often can't be solved in closed form.

The raison d’etre of Love et al is to replace the system with a perfectly conducting surface and an EM field. Any electric fields along (tangential) to the surface vanish as they can't generate any current so can't radiate so their contribution is zero hence reducing the number of integrations. Any normal to the surface do contribute and must be calculated.

You start with the electric field and compute the current density and if you have chosen you surface well elements of the current density don't contribute.

I will also 'nail my colours to the mast' by saying I am a big fan of using equivalence methods in theoretical physics as they often reveal beautiful symmetries and give real insight but I am not a big fan of their use in areas such as antennae design because they assume things such as a perfect conductor (i.e. one which will kill any electric current on the surface) or worse a surface which will kill any magnetic field on the surface. Thus to transition to the real world (conductors with resistance etc.) takes as much work as solving the problem directly.

You may find chapters 5 & 6 of http://www.plasma.uu.se/CED/Book/EMFT_Book.pdf a better text

for the more practical approach, if that suits you, try the IEEE Antennas and Propagation Mag report reproduced at http://www.csun.edu/~hceen002/paper1.pdf

Hope this helps

Regards

Sam

5. Apr 13, 2012

### eliotsbowe

That was helpful, thanks a lot!