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184_notes:loop [2018/11/01 21:28] – dmcpadden184_notes:loop [2022/04/04 12:46] (current) – hallstein
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 Section 21.6 in Matter and Interactions (4th edition) Section 21.6 in Matter and Interactions (4th edition)
  
-[[184_notes:i_thru|Next Page: Current through a Loop]]+/*[[184_notes:i_thru|Next Page: Current through a Loop]]
  
-[[184_notes:motiv_amp_law|Previous page: Motivating Ampere's Law]]+[[184_notes:motiv_amp_law|Previous page: Motivating Ampere's Law]]*/
  
 ===== Magnetic field along a closed loop ===== ===== Magnetic field along a closed loop =====
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 As you have seen before, the [[184_notes:moving_q|magnetic field circulates around a moving charge]]. Below is a simulation that shows this for a series of moving point charges. As you have seen before, the [[184_notes:moving_q|magnetic field circulates around a moving charge]]. Below is a simulation that shows this for a series of moving point charges.
  
-{{url>http://web.pa.msu.edu/people/caballero/teaching/simulations/MagneticFieldCirculation.html 675px,425px|Charges moving along a line}}+{{url>https://web.pa.msu.edu/people/caballero/teaching/simulations/MagneticFieldCirculation.html 675px,425px|Charges moving along a line}}
  
 As you can see, the sizes of the magnetic field vectors (the arrows) get larger as the charges get closer to the observation locations and get smaller as they pass and move away. The direction of the magnetic field is always around the path of the charges. Now, imagine a constant stream of particles very close together, that is, a current of many electrons moving in a wire. In that case, the direction of the magnetic field is still around the wire, but the magnitude stays constant. That is, **for a steady current, the magnetic field at any one point is a constant in time**. Furthermore, **for cylindrical wires (the ones we will focus on), the magnitude of magnetic field is constant for a given distance from the wire**. You saw this with the long wire when we solved the problem using Biot-Savart.  As you can see, the sizes of the magnetic field vectors (the arrows) get larger as the charges get closer to the observation locations and get smaller as they pass and move away. The direction of the magnetic field is always around the path of the charges. Now, imagine a constant stream of particles very close together, that is, a current of many electrons moving in a wire. In that case, the direction of the magnetic field is still around the wire, but the magnitude stays constant. That is, **for a steady current, the magnetic field at any one point is a constant in time**. Furthermore, **for cylindrical wires (the ones we will focus on), the magnitude of magnetic field is constant for a given distance from the wire**. You saw this with the long wire when we solved the problem using Biot-Savart. 
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 === Symmetry is critical === === Symmetry is critical ===
  
-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]].
  
 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:
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