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I am working on AP problem 1993B3, but I am having a really hard time. the problem is:
A particle of mass m and charge q is accelerated from rest in the plane of the page through a potential difference V between two parallel plates. the particle is injected through a hole in the right-hand plates into a region of space containing a uniform magnetic field of magnitude B oriented perpendicular to the plane of the page. the particle curves in a semicircular path and strikes a detector.
A. I) State whether the sign of the charge on the particle is + or -
II) State whether the direction of the magnetic field is into the page or out
B. Determine the following in terms of m, q, V, and B
I) the speed of the charged particle as it enters the region of field B
II) the force exerted on the charged particle by field B
III) the distance from the point of injection to the detector
IV) the work done by the field on the charged particle during the semicircular trip
Here is where I have gotten:
A. I) the charge would have to be positive (i used the right hand rule)
II) out of the page (right hand rule again)
B. I) I have tried a bunch of different things such as setting qvB = (mv^2)/r (which i now know is not right), using the B= uknot/2 X I/r and setting it equal to all sorts of things...I am totally confused and have no idea what to try next...
II) I think that you would use F=qVB and just plug in your answer from above into V and solve, right?
III)here is what i tried if you can follow it ![]()
B=(uknot/2)(I/r) -> B=2pi (I/r) -> I=P/v so B=2pi (p/vr) -> p=mv so B= 2pi (m/r) so r = (2pi m)/B and then that times 2 since the distance would be 2r.
IV) w= qEd maybe? I have no idea
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For BI, you are right. Since the particle hasn't started moving in a circular path yet, then you can't do what you have done. Also, the magnetic field hasn't effected the particle yet. You just have two big plates accelerating it. Ignoring the hole, what would be the particles speed when it slammed into the right plate?
Think conservation of energy:
You can get the rest from there.
Your thinking on BII I believe is OK.
BIII: The particle goes in a semi-circular path, so if you know the radius (which you found) then you can figure out the distance traveled -- half circumference.
BIV: This is why I LOVE the AP exam! ANY particle moving through a magnetic field will have NO work done on it by the field because the magnetic force is ALWAYS at right angles to the direction of motion.
Keep that in mind, because something like it WILL be on the AP.
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I have expanded on my comments on this topic here:
http://www.ilovephysics.com/2009/04/20/ … tic-field/
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