(a) Show that the frequency of any mode (E,B) of a resonant cavity with volume V can...
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(a) Show that the frequency of any mode (E,B) of a resonant cavity with volume V can be computed from
(b) Suppose E → E + δE or B → B + δB, where δE and δB satisfy the boundary conditions. Prove that the change in ω2 is only second-order in δE or δB. This implies that any choice of E(r) or B(r) in these formulae which satisfies the boundary conditions (but not the Maxwell equations) provides an upper bound on the lowest mode frequency.
(c) Obtain an estimate of the lowest TM-mode frequency in a cylindrical cavity of radius R by minimizing the frequency with respect to the variational parameter a in the choice B = (ρ + aρ2)ϕ̂ . Compare your answer with the exact result.
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b Suppose E E or B B where E and B satisfy the boundary conditions Prove that the change in u2 i...View the full answer
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NEETA SINGH
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