Hi everyone ! This is my first post! How can we prove that during the reflection of an electromagnetic wave on the surface of a perfect conductor, the magnetic field [itex] \vec{b} [/itex] acting on a surface element [itex] ds [/itex] is worth half the total magnetic field [itex] \vec{B} [/itex] using Ampere's Law. That is [itex] \vec{b}=\frac{1}{2}\vec{B} [/itex]. This in order to justify the one half factor in the expression of the force acting on [itex] ds [/itex] which is [itex] d\vec{f}=\frac{1}{2}\vec{j_{s}}\times \vec{B} \cdot ds[/itex], where [itex]\vec{j_{s}}[/itex] is the surface current density on the conductor. A drawing would be welcome. Thanks in advance for your answers PS: Why does it automatically go to a new line when i insert a Latex equation?
When you want an equation to appear "in line", use "itex" in the opening and closing tags, not "tex".
There's maybe another way to justify the [itex]\frac{1}{2}[/itex] factor without using AmpĂ¨re's law ? It's how it was justified in my textbook but I couldn't understand it. Anyone ?
Consider a sheet of surface current K: KKKKKKKKKKKKKKKKKKKKKKKKKK with the EM wave incident from above. The B field comes from two sources 1) the wave B_W, and 2)the current, B_K. Below the surface (in the metal) B is zero. That mean the two components of B cancel so B_W=B_K in magnitude and opposite in sign. Above the surface, B_K changes sign, but B_W doesn't, so the total B field outside is twice the field B_W which acts on the surface current.