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arierreF
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Homework Statement
A particle of charge −q is moving with a velocity [itex]\vec{v}[/itex]. It then enters midway between two plates where there exists a uniform magnetic field pointing into the page, as shown in attached image.
Homework Equations
[itex]\vec{F_{B}} = q\vec{v}\times\vec{B}[/itex]
The Attempt at a Solution
I discovered that the charged particle is going to be deflected downward. Then it is going to strike the bottom plate before leaving the region between two plates. So the distance between the end of the bottom plate and where the particle strikes is what this problem is asking for.
See the following attached image.
[itex]y = 0[/itex] because it strikes the end of the plate.
[itex]y_{0} = \frac{d}{2}[/itex]
so [itex]t = \sqrt{da}[/itex]
[itex]\vec{F_{B}} = q\vec{v}\times\vec{B}[/itex]
to find the magnitude of acceleration:[itex]ma = qvB[/itex]
[itex]a = \frac{qvB}{m}[/itex]
then [itex]t = \sqrt{d\frac{qvB}{m}}[/itex]
[itex]x = x_{0} + v_{0}t[/itex]
[itex]x_{0} = 0[/itex]
[itex]x= v_{0}t[/itex]
because [itex]v_{0} = v[/itex]
[itex]x = v\sqrt{d\frac{qvB}{m}}[/itex]Then the distance is [itex]l- v\sqrt{d\frac{qvB}{m}}[/itex]Is that correct? cause i have feeling that it is wrong.
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