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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F590efbb4-bfa3-48e4-b7a4-ba8d0f00ec23%2F3bff58dc-6d0d-4823-964c-1a0176b5a6eb%2Fgakyder_processed.jpeg&w=3840&q=75)
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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