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184_notes:examples:week10_radius_motion_b_field [2017/11/02 21:21] – dmcpadden | 184_notes:examples:week10_radius_motion_b_field [2018/07/03 14:01] (current) – curdemma | ||
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=====Radius of Circular Motion in a Magnetic Field===== | =====Radius of Circular Motion in a Magnetic Field===== | ||
Suppose you have a moving charge $q>0$ in a magnetic field $\vec{B} = -B \hat{z}$. The charge has a velocity of $\vec{v} = v\hat{x}$, and a mass $m$. What does the motion of the charge look like? What if the charge enters the field from a region with $0$ magnetic field? | Suppose you have a moving charge $q>0$ in a magnetic field $\vec{B} = -B \hat{z}$. The charge has a velocity of $\vec{v} = v\hat{x}$, and a mass $m$. What does the motion of the charge look like? What if the charge enters the field from a region with $0$ magnetic field? | ||
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* We represent the two situations below. | * We represent the two situations below. | ||
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====Solution==== | ====Solution==== | ||
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$$\vec{F}= q (v\hat{x}) \times (-B\hat{z}) = qvB\hat{y}$$ | $$\vec{F}= q (v\hat{x}) \times (-B\hat{z}) = qvB\hat{y}$$ | ||
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So, the force on the charge is at first perpendicular to its motion. This is pictured above. You can imagine that as the charge' | So, the force on the charge is at first perpendicular to its motion. This is pictured above. You can imagine that as the charge' | ||
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So now we know the radius. You can imagine that if the particle entered from outside the region of magnetic field, it would take the path of a semicircle before exiting the field in the opposite direction. Below, we show what the motion of the particle would be in each situation. | So now we know the radius. You can imagine that if the particle entered from outside the region of magnetic field, it would take the path of a semicircle before exiting the field in the opposite direction. Below, we show what the motion of the particle would be in each situation. | ||
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