# What is a magnetic wall?

I've been going through the "Foundations for microwave engineering" textbook by Robert E. Collin in order to study coplanar waveguides. In doing so I was introduced to Conformal mapping techniques, a beautiful way of calculating the capacitance of such systems by exploiting the Schwarz-Christoffel transformations.

In doing the derivation it states that the "By symmetry the two boundaries are magnetic walls on which $$\frac{d\phi}{dv}=0$$". Here v is the imaginary part of the complex plane, yet it can be seen as the physical y direction. Without worrying about the symmetry, what does it mean by magnetic walls? there seems to be no answer on the internet.

• Can you share a diagram, showing which direction is called "y" relative to the dimensions of the waveguide? – The Photon Jul 22 '19 at 21:58

Magnetic wall usually means "perfect magnetic conductor" (PMC), which is the dual (or magnetic analogue) of a perfect electric conductor. Inside the PMC, $$\vec{H} = 0$$ and $$\rho_m = 0$$, where $$\rho_m$$ is the magnetic charge density.
The boundary conditions for a PMC are $$\hat{n} \times \vec{E} = -\vec{K}_m$$ $$\hat{n} \times \vec{H} = 0$$ $$\hat{n} · \vec{D} = 0$$ $$\hat{n} · \vec{B} = \rho_m$$ where $$\hat{n}$$ is the outward unit normal vector and $$\vec{K}_m$$ is the magnetic surface charge density.
The text you quote is defining the term. The "magnetic wall" is a surface on which $$\frac{d\phi}{dv}=0$$.