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| 184_notes:symmetry [2020/08/24 19:26] – dmcpadden | 184_notes:symmetry [2021/07/06 17:51] (current) – bartonmo |
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| {{youtube>I4Utm80K8hM?large}} | {{youtube>I4Utm80K8hM?large}} |
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| ==== Gauss' Law ==== | ===== Gauss' Law ===== |
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| [[184_notes:gauss_motive|Gauss' Law]] helps us to calculate the electric field when there is sufficient symmetry to use it. That is, Gauss' Law, as mathematical statement, is always true, but it's only useful in limited cases (namely, for planes, cylinders and spheres of charge). The total electric flux is always proportional to the enclosed charge, but that doesn't mean we can always calculate the electric field from Gauss' Law. | [[184_notes:gauss_motive|Gauss' Law]] helps us to calculate the electric field when there is sufficient symmetry to use it. That is, Gauss' Law, as mathematical statement, is always true, but it's only useful in limited cases (namely, for planes, cylinders and spheres of charge). The total electric flux is always proportional to the enclosed charge, but that doesn't mean we can always calculate the electric field from Gauss' Law. |
| where we understand the direction to point radially outward as usual for a positive point charge. This was necessary to argue the simplification of Gauss' Law from the first to the second line. | where we understand the direction to point radially outward as usual for a positive point charge. This was necessary to argue the simplification of Gauss' Law from the first to the second line. |
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| ==== Ampere's Law ==== | ===== Ampere's Law ===== |
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| [[184_notes:motiv_amp_law|Ampere's Law]] helps us calculate the magnetic field when there is sufficient symmetry to use it. Like Gauss' Law, Ampere's Law, as a mathematical statement, is always true, but it's only useful in limited contexts (like long wires or solenoids). The total integral around any closed loop is always proportional to the total current enclosed by the loop, but that doesn't mean we can compute the magnetic field using Ampere's Law for every case, | [[184_notes:motiv_amp_law|Ampere's Law]] helps us calculate the magnetic field when there is sufficient symmetry to use it. Like Gauss' Law, Ampere's Law, as a mathematical statement, is always true, but it's only useful in limited contexts (like long wires or solenoids). The total integral around any closed loop is always proportional to the total current enclosed by the loop, but that doesn't mean we can compute the magnetic field using Ampere's Law for every case, |