Question: (a) Calculate the induced surface charge density TM and the longitudinal surface current density K TM associated with the propagation of a TM mode

(a) Calculate the induced surface charge density σ_TM and the longitudinal surface current density K_TM associated with the propagation of a TM mode in a perfectly conducting waveguide with a uniform cross section. Show that K_TM= ν_pσTMẑ where ν_pis the phase velocity of the wave propagating in the z-direction.
(b) Calculate the induced surface charge density σ_TEand the surface current density K_TEassociated with the propagation of a TE mode in a perfectly conducting waveguide with a uniform cross section. Show that ẑ · K_TE= vgσ_TEwhere ν_g is the group velocity of the wave.
(c) Show that in the TE case a surface current appears in the transverse direction also.(d) Show that the surface current and surface charge satisfy a “surface continuity equation” for both TE and TM modes.

(t = x 2)

Step by Step Solution

★★★★★

3.53 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Surface charge density and longitudinal surface current density for TM mode For a TM Transverse Magnetic mode in a perfectly conducting waveguide wi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Modern Electrodynamics Questions!

Infinite line x = 3, z = 4 carries 16nC/m and is located in free space above the conducting plane z = 0. (a) Find E at (2, 2, 3). (b) Calculate the induced surface charge density on the conducting...

Derive Equation 26.33 for the induced surface charge density on the dielectric in a capacitor. Equation 26.33 nol 1 Ninduced

A point charge q lies a distancer > R from the center of an uncharged, conducting sphere of radius R. Express the induced surface charge density in the form where is the polar angle measured from a...

Waveguide Charge and Current (a) Calculate the induced surface charge density OTM and the longitudinal surface current density KTM associated with the propagation of a TM mode in a perfectly...

The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the...

E-Physics Tutorial Book Note: I have attached below the lesson for the 3 activities. Thank you so much for your time and effort. Activity 1. Directions: Use the right-hand rule to determine the...

I have attached the 10-K FORM of the focus company, The Container Store Group, Inc with the question. Please open the attachment PDF file of the 10- K FORM which i have enclosed with the question as...

(20 points) A metal-like disk of radius a and dielectric constant e, spins with an angular velocity about its axis in a uniform axial field B. (a) Explain why the disk will polarize. (b) Derive a...

Please answer all the following items (1, 2, 3, 4, 5). Please show your complete solution and the formula that you use to find the answer. Thank you so much. 1. Find the magnitude of the emf induced...

Compute the following: Compute the following: ( 4 0 points ) A uniform surface load of 1 5 0 0 p s f is applied over the rectangular shape shown below. Determine the increase in stress 1 5 f t below...

James Maciel leased an apartment in Regent Village, a university- owned housing facility for Regent University (RU) students in Virginia Beach, Virginia. The lease ran until the end of the fall...

An audit teams purpose in reviewing the documentation concerning the renewal of a note payable shortly after the balance- sheet date most likely is to obtain evidence concerning managements...