Please explain why A_m B_m C_m D_m = 0
by orthogonality in the following expressions:
For reference, here is the main question (I do not need this
answered; I already have it solved. I just need help
understanding the orthogonality stuff above. Thanks!
Electrostatics: Multipoles (based on a problem in graduate
Electrodynamics by JD Jackson).
-m = p>b m т 01 = A + Amp cos(mo) – Eop coso, 02 = Bo + Co log p+(BmpM + Cmp-m) cos(mo), a <p<b α<<b 03 = Do + Dmp cos(mo), Φ = = m = ρ<α m For each value of m, there are four unknowns, Am, Bm, Cm and Dm. On the other hand, there are also four matching conditions (D+ and Ell both at a and at b). Note, however, that when m + 1 these matching conditions yield homogeneous equations which only admit the trivial solution Am : Bm = = : Cm = Dm = 0 m #1 т
A very long, right circular, cylindrical shell of dielectric constant e/o and inner and outer radii a and b, respectively, is placed in a previously uniform electric field Eo with its axis perpendicular to the field. The medium inside and outside the cylinder has a dielectric constant of unity.
Please explain why A_m B_m C_m D_m = 0 by orthogonality in the following expressions: For reference, here is the mai
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