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| 184_notes:loop [2022/04/04 12:40] – hallstein | 184_notes:loop [2022/04/04 12:46] (current) – hallstein |
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| === Symmetry is critical === | === Symmetry is critical === |
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| The structure (or symmetry) of this field is very useful for Ampere's Law. That is, the fact that the B-field always circulates around the wire and is the same magnitude for a given distance makes this problem of a steady state line of charge an excellent candidate for using Ampere's Law. //In fact, this symmetry holds inside the wire as well//. That is, there will be a constant magnitude magnetic field circulating around every point inside the wire as well! This is a really important result that we can explore with Ampere's Law, but that can be a real challenge to deal with using [[184_notes:b_current|Biot-Savart]]. | The structure (or symmetry) of this field is very useful for Ampere's Law. That is, the fact that the B-field always circulates around the wire and is the same magnitude for a given distance makes this problem of a steady state current an excellent candidate for using Ampere's Law. //In fact, this symmetry holds inside the wire as well//. That is, there will be a constant magnitude magnetic field circulating around every point inside the wire as well! This is a really important result that we can explore with Ampere's Law, but that can be a real challenge to deal with using [[184_notes:b_current|Biot-Savart]]. |
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| We'll start by thinking about the magnetic field outside a wire and the mathematical representation Ampere's Law: | We'll start by thinking about the magnetic field outside a wire and the mathematical representation Ampere's Law: |