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184_notes:q_path [2018/07/03 13:11] – curdemma | 184_notes:q_path [2021/06/10 01:13] – bartonmo | ||
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Section 20.1 in Matter and Interactions (4th edition) | Section 20.1 in Matter and Interactions (4th edition) | ||
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===== Path of a Charge through a Magnetic Field ===== | ===== Path of a Charge through a Magnetic Field ===== | ||
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{{youtube> | {{youtube> | ||
- | ==== Path of the Moving Charge ==== | + | ===== Path of the Moving Charge |
- | {{ 184_notes: | + | [{{ 184_notes: |
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: | 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: | ||
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$$\vec{p}_f | $$\vec{p}_f | ||
- | {{184_notes: | + | [{{184_notes: |
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), | 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), | ||
- | ==== Work Done ==== | + | ===== Work Done ===== |
- | {{ 184_notes: | + | [{{ 184_notes: |
You may be wondering if there is a magnetic potential energy associated with the magnetic field (after all [[184_notes: | You may be wondering if there is a magnetic potential energy associated with the magnetic field (after all [[184_notes: | ||
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This also means that we do not have a way to define a magnetic potential or a magnetic potential energy in the same way that we did with electric fields. It turns out that we can define a [[https:// | This also means that we do not have a way to define a magnetic potential or a magnetic potential energy in the same way that we did with electric fields. It turns out that we can define a [[https:// | ||
- | ==== Examples ==== | + | ===== Examples |
[[: | [[: | ||
[[: | [[: |