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--- 184_notes:magnetic_field [2021/07/06 17:30] – bartonmo
+++ 184_notes:magnetic_field [2021/07/06 17:31] (current) – bartonmo
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 The direction of the force is determined by the [[184_notes:rhr|right hand rule]] and is perpendicular to the plane defined by the vector velocity and magnetic field. This means that a charge will experience no magnetic force if it travels directly along a magnetic field line (or opposite it).
-==== Collections of moving charges ====
+===== Collections of moving charges =====
 [{{  184_notes:week9_5.png?300|Magnetic field from a line of charge}}]
@@ Line 42: / Line 42: @@
 We can use this integration technique analytically and computationally to find the magnetic field produce by a distribution of current - either through [[184_notes:examples:week10_current_segment|a wire segment]], [[184_notes:b_current|a very long wire]], or [[184_notes:examples:week10_current_ring|loops of wires]].
-==== Effects and Applications ====
+===== Effects and Applications =====
 The fact that moving charges generate magnetic fields, that they superpose, and that other moving charges experience magnetic forces in the presence of a magnetic field result in a number of different magnetic phenomenon. Some are quite practical. Some of the most important ones are discussed below:
 [{{  184_notes:bfieldlongwire.png?200|Magnetic field around a current carrying wire}}]
-=== Current-carrying wires ===
+===== Current-carrying wires =====
 Wires that carry current will produce magnetic fields that circulate around them. This stems from the superposed magnetic fields from all the little charges moving in the wire. This can be quite important because those magnetic fields might disturb other sensitive electronics in a particular electronic device or experiment. Moreover, [[184_notes:examples:week12_force_between_wires|pairs of current carrying wires can exert forces on each other]] (attractive or repulsive) causing physical stress on the wires or other components.
-=== Curved motion ===
+===== Curved motion =====
 [{{  184_notes:week11_5.png?300|Motion of a charge moving through a magnetic field}}]
@@ Line 57: / Line 57: @@
 This is a very useful result in cyclotron accelerators where a magnetic field is used to force charged particles into a circular path (while an electric field is used to speed up the charged particles). The circular path (made by the magnetic field) helps contain the accelerator to a smaller area. We can also exploit the tendency to have curved trajectories in mass spectrometers, which can be used to determine the charge to mass ratio of a particle, as particles with different charge-to-mass ratios will curve differently. Using electric and magnetic fields together, we can manipulate the trajectories of charged particles in ways that help us select out only certain kinds of particles; this is used in particle accelerators, but also in simpler situations like cathode-ray screens (which used to be in the big square tv's and computer monitors but have gone out of fashion lately).
-=== Changing magnetic fields ===
+===== Changing magnetic fields =====
 Much of our study of magnetic fields focused on fields due to steady currents, that is, magnetic fields that didn't change with time. The field was produced a steady stream of charge carriers that we modeled as moving with the same speed and direction. This doesn't have to be the case and it's quite common that it isn't.