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Lecture 27
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FYS3120 – Classical mechanics and electrodynamics
Recap The magnetostatic solution for the potential is At large distances from the current this can be approximated in the multipole expansion where the monopole contribution is A0 = 0. The force and torque from external fields are 𝐴 𝑟 = μ 0 4π 𝑗 𝑟 𝑟 − 𝑟 ′ 𝑑 3 𝑟 ′ 𝐴 𝑟 = 𝐴 0 𝑟 𝐴 1 𝑟 𝐴 2 𝑟 +... Lav totalenergi første tilgjengelig eksperimentelt i våre dager. 𝐹 𝑒 = 𝑄 𝐸 + 𝑝 ⋅ ∇ 𝐸 , τ 𝑒 = 𝑝 × 𝐸 𝐹 𝑚 = 𝑚 ⋅ ∇ 𝐵 , τ 𝑚 = 𝑚 × 𝐵 / Are Raklev / FYS3120 – Classical mechanics and electrodynamics
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FYS3120 – Classical mechanics and electrodynamics
Today Solution to time dependent sources Green’s functions (light). Fourier transformation to Helmholtz’ equation. Solution in terms of retarded sources. / Are Raklev / FYS3120 – Classical mechanics and electrodynamics
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FYS3120 – Classical mechanics and electrodynamics
Summary The scalar and vector potential for time- dependent sources is where the time for the source is the retarded time ϕ 𝑟 ,𝑡 = 1 4π ϵ ρ 𝑟 , 𝑡 − 𝑟 − 𝑟 ′ 𝑑 3 𝑟 ′ 𝐴 𝑟 ,𝑡 = μ 0 4π 𝑗 𝑟 , 𝑡 − 𝑟 − 𝑟 ′ 𝑑 3 𝑟 ′ Lav totalenergi første tilgjengelig eksperimentelt i våre dager. 𝑡 − = 𝑡 − 𝑟 − 𝑟 ′ 𝑐 / Are Raklev / FYS3120 – Classical mechanics and electrodynamics
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