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Find the fields, and the charge and current distributions, corresponding to 1 qt V(r, t) = 0; A(r, t) = 4ntо r2 Î

Find the fields, and the charge and current distributions, corresponding to 1 qt V(r, t) = 0; A(r, t) = 4ntо r2 Î

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Problem 7.35 Please write
Function A, we can with impunity add VA to A, we provided e simultaneously subtract aλ/at from V. None of this will affect the physi- cal quantities E and B. Such changes in V and A are called gauge transformations. "ugly" equations (7.65) and (7.66). In magnetostatics, it was best to choose V A = 0 They can be exploited to adjust the divergence of A, with a view to simplifying the (equation (5.55)); in electrodynamics the situation is not so clear-cut, and the most convenient gauge depends to some extent on the problem at hand. There are many famous gauges in the literature; I'll just show you the two most popular ones. . Conce Problem 7.35 Find the fields, and the charge and current distributions, corresponding to 1 qt F V(r, t) = 0; A(r, t) = Problem 7.36 Suppose V = 0 and A = Ao sin(kx - wt)j, where Ao, w, and < are constants. Find E and B, and check that they satisfy Maxwell's equations in vacuum. What condi- tion must you impose on w and K? 4πEO ² = Problem 7.37 Use the gauge function A :-(1/4 Teo) (qt/r) to transform the potentials in Problem 7.35, and comment on the result. 7.4.3 Coulomb Gauge and Lorentz Gauge The Coulomb gauge. As in magnetostatics, we pick (7.68)
Transcribed Image Text:Function A, we can with impunity add VA to A, we provided e simultaneously subtract aλ/at from V. None of this will affect the physi- cal quantities E and B. Such changes in V and A are called gauge transformations. "ugly" equations (7.65) and (7.66). In magnetostatics, it was best to choose V A = 0 They can be exploited to adjust the divergence of A, with a view to simplifying the (equation (5.55)); in electrodynamics the situation is not so clear-cut, and the most convenient gauge depends to some extent on the problem at hand. There are many famous gauges in the literature; I'll just show you the two most popular ones. . Conce Problem 7.35 Find the fields, and the charge and current distributions, corresponding to 1 qt F V(r, t) = 0; A(r, t) = Problem 7.36 Suppose V = 0 and A = Ao sin(kx - wt)j, where Ao, w, and < are constants. Find E and B, and check that they satisfy Maxwell's equations in vacuum. What condi- tion must you impose on w and K? 4πEO ² = Problem 7.37 Use the gauge function A :-(1/4 Teo) (qt/r) to transform the potentials in Problem 7.35, and comment on the result. 7.4.3 Coulomb Gauge and Lorentz Gauge The Coulomb gauge. As in magnetostatics, we pick (7.68)
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