184_notes:q_path

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184_notes:q_path [2018/07/03 13:11] – curdemma184_notes:q_path [2018/07/03 14:00] – curdemma
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 ==== Path of the Moving Charge ==== ==== Path of the Moving Charge ====
  
-{{  184_notes:week11_3.png?150}}+[{{  184_notes:week11_3.png?150|Force felt by a charge moving through a B field in the -x direction}}]
  
 Let's start by considering a charge moving to the left ($-\hat{x}$ direction) in a magnetic field that points into the page ($-\hat{z}$ direction). Using the right hand rule, we can figure out that the force on this charge is down ($-\hat{y}$ direction). So what does this mean for the path of our charge? We can use the [[183_notes:momentum_principle|momentum principle]] to help us figure it out. The momentum principle says that: Let's start by considering a charge moving to the left ($-\hat{x}$ direction) in a magnetic field that points into the page ($-\hat{z}$ direction). Using the right hand rule, we can figure out that the force on this charge is down ($-\hat{y}$ direction). So what does this mean for the path of our charge? We can use the [[183_notes:momentum_principle|momentum principle]] to help us figure it out. The momentum principle says that:
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 $$\vec{p}_f  = \vec{F}_{net,avg} \Delta t + \vec{p}_i$$ $$\vec{p}_f  = \vec{F}_{net,avg} \Delta t + \vec{p}_i$$
  
-{{184_notes:week11_4.png?150  }}+[{{184_notes:week11_4.png?150|Force changes the direction of the velocity  }}]
 This means that if our magnetic force is pushing the charge down for a short time, the velocity of the charge will then point slightly down. If we do the same process at the next location and the next location (it turns out a computer is pretty good at doing these calculations), we find that **the charge will move in a circle**, with the magnetic force always pointing toward the center of the circular path. It turns out that this is a perfect example of [[183_notes:ucm|uniform circular motion]].  This means that if our magnetic force is pushing the charge down for a short time, the velocity of the charge will then point slightly down. If we do the same process at the next location and the next location (it turns out a computer is pretty good at doing these calculations), we find that **the charge will move in a circle**, with the magnetic force always pointing toward the center of the circular path. It turns out that this is a perfect example of [[183_notes:ucm|uniform circular motion]]. 
  
  
 ==== Work Done ==== ==== Work Done ====
-{{  184_notes:week11_5.png?400}}+[{{  184_notes:week11_5.png?400|Trajectory of a particle moving through a constant magnetic field at a constant speed}}]
  
 You may be wondering if there is a magnetic potential energy associated with the magnetic field (after all [[184_notes:pc_energy|we did use the electric force to get to electric potential energy]]). We can figure this out by first looking at the work done by the magnetic field on the charge. Remember that [[183_notes:work_by_nc_forces|the general equation for work]] is given by: You may be wondering if there is a magnetic potential energy associated with the magnetic field (after all [[184_notes:pc_energy|we did use the electric force to get to electric potential energy]]). We can figure this out by first looking at the work done by the magnetic field on the charge. Remember that [[183_notes:work_by_nc_forces|the general equation for work]] is given by:
  • 184_notes/q_path.txt
  • Last modified: 2021/07/07 14:37
  • by schram45