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Problem 1. A medium is described by a dielectric function ɛ, a conductivity o , and a permeability 4, all of which are scalars and independent of both time and position. The medium contains a charge density p(ï,t). However, the current density is not independent, but is given by j(7,t) = oĒ(7,t). Work the following in egs units (you'll rework this in SI units in Prob. 2.) ) Define the Lorentz gauge, which for o ± 0 now has an extra term relative to the expression that you may have seen before. However, show that even with the extra term, the same operator applies to both A and ø. Which of these two equations is inhomogeneous?

Problem 1. A medium is described by a dielectric function ɛ, a conductivity o , and a permeability 4, all of which are scalars and independent of both time and position. The medium contains a charge density p(ï,t). However, the current density is not independent, but is given by j(7,t) = oĒ(7,t). Work the following in egs units (you'll rework this in SI units in Prob. 2.) ) Define the Lorentz gauge, which for o ± 0 now has an extra term relative to the expression that you may have seen before. However, show that even with the extra term, the same operator applies to both A and ø. Which of these two equations is inhomogeneous?

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Problem 1. A medium is described by a dielectric function ɛ, a conductivity o , and a permeability 4, all of which are scalars and independent of both time and position. The medium contains a charge density p(ï,t). However, the current density is not independent, but is given by j(7,t) = oĒ(7,t). Work the following in egs units (you'll rework this in SI units in Prob. 2.) ) Define the Lorentz gauge, which for o ± 0 now has an extra term relative to the expression that you may have seen before. However, show that even with the extra term, the same operator applies to both A and ø. Which of these two equations is inhomogeneous?
Transcribed Image Text:Problem 1. A medium is described by a dielectric function ɛ, a conductivity o , and a permeability 4, all of which are scalars and independent of both time and position. The medium contains a charge density p(ï,t). However, the current density is not independent, but is given by j(7,t) = oĒ(7,t). Work the following in egs units (you'll rework this in SI units in Prob. 2.) ) Define the Lorentz gauge, which for o ± 0 now has an extra term relative to the expression that you may have seen before. However, show that even with the extra term, the same operator applies to both A and ø. Which of these two equations is inhomogeneous?
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