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184_notes:q_path [2017/10/25 22:34] – dmcpadden | 184_notes:q_path [2020/08/23 21:28] – dmcpadden | ||
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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 ===== | ||
We just talked about the force that a moving charge feels when it travels through a magnetic field. So now the question remains: what happens to the charge when it feels this force? Since the magnetic force is perpendicular to the velocity of the charge, we will show that the charge actually begins to move in a circular pattern. | We just talked about the force that a moving charge feels when it travels through a magnetic field. So now the question remains: what happens to the charge when it feels this force? Since the magnetic force is perpendicular to the velocity of the charge, we will show that the charge actually begins to move in a circular pattern. | ||
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==== Path of the Moving Charge ==== | ==== Path of the Moving Charge ==== | ||
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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 | ||
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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 ==== | ||
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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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==== Examples ==== | ==== Examples ==== | ||
- | Find the radius | + | [[: |
- | Helix things - spiral path... | + | [[: |