TE Waves in Rectangular Wave Guide

[unscientific]

Hi guys I'm having difficulty understanding why the boundary conditions lead to dX/dx = 0.

Why must B_x = 0 at x = 0 and x = a?

 

[Meir Achuz]

B_n is continuous at a boundary, and B=0 inside a perfect conductor (which is assumed for these equations).
Therefor B_n=0 just outside the conductor.

 

[buoyant]

And that is arisen from the fact that there is no magnetic dipole, i.e., the magnetic field is divergenceless. You can derive the continuity of the normal component of the magnetic field on the boundary by imaging a small pillbox on the boundary. Maybe Griffiths already described in Chap 5.

 

[Meir Achuz]

And that is arisen from the fact that there is no magnetic dipole,

I know you meant monopole.

 

[buoyant]

Thanks Achuz for noticing my mistake

 

[unscientific]

B_n is continuous at a boundary, and B=0 inside a perfect conductor (which is assumed for these equations).
Therefor B_n=0 just outside the conductor.

Sorry, I don't get what you mean. If B_n is perpendicular to surface and = 0, then won't B_x = 0 and B_y = 0 along y-axis and x-axis correspondingly

 

[scoobmx]

Sorry, I don't get what you mean. If B_n is perpendicular to surface and = 0, then won't B_x = 0 and B_y = 0

Only the normal component is continuous.. so B is parallel to surface at the boundary.

 

[unscientific]

Only the normal component is continuous.. so B is parallel to surface at the boundary.

Yes, so along x-axis, B_y = 0, and along y-axis, B_x = 0?

 

[Meir Achuz]

Yes...