03/20/2015PHY 712 Spring 2015 -- Lecture 221 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 22: Start reading Chap. 9 A.Electromagnetic.

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Presentation transcript:

03/20/2015PHY 712 Spring Lecture 221 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 22: Start reading Chap. 9 A.Electromagnetic waves due to specific sources B.Dipole radiation patterns

03/20/2015PHY 712 Spring Lecture 222

03/20/2015PHY 712 Spring Lecture 223

03/20/2015PHY 712 Spring Lecture 224 Formulation of Maxwell’s equations in terms of vector and scalar potentials

03/20/2015PHY 712 Spring Lecture 225 Formulation of Maxwell’s equations in terms of vector and scalar potentials -- continued

03/20/2015PHY 712 Spring Lecture 226 Solution of Maxwell’s equations in the Lorentz gauge -- continued

03/20/2015PHY 712 Spring Lecture 227 Electromagnetic waves from time harmonic sources

03/20/2015PHY 712 Spring Lecture 228 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 229 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2210 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2211 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2212 Forms of spherical Bessel and Hankel functions:

03/20/2015PHY 712 Spring Lecture 2213 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2214 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2215 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2216 Electromagnetic waves from time harmonic sources – continued: Note: in this case we have assumed a restricted extent of the source such that kr’<<1.

03/20/2015PHY 712 Spring Lecture 2217 Electromagnetic waves from time harmonic sources – continued:

03/20/2015PHY 712 Spring Lecture 2218 Example of dipole radiation source

03/20/2015PHY 712 Spring Lecture 2219 Example of dipole radiation source -- continued Relationship to pure dipole approximation (exact when kR  0)