- #1
pollytheparrot
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Homework Statement
Basically there are 3 plate capacitors, with a distance a between the first two and b between the last two. In between the first two plates is voltage V. A particle of charge q is released from the first plate, and when it leaves the second plate it is no longer accelerating. There is a magnetic field of B in the second part, and then a hole of radius r at the third plate, find the distance that the particle drops due to the magnetic field. I neglected to outline this specifically in the picture, but basically it is the distance of the bottom black line and could be called "d"
Homework Equations
U=K
F=qv x B
Sum F = ma
a=v^2/r
E=qV
The Attempt at a Solution
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First I had to find the velocity of the particle at the point of the first plate, and did this using conservation of energy.
U=K
qV=.5mv^2
v=sqrt(2qV/m)
Second, is finding the radius of the circle in the second part, using F=ma and angular acceleration
Then Sum F = ma, only force is magnetic
qv x B = ma
qv x B = m(v^2/R)
R=m*v^2 / q*v*B
R=m*(2qV/m) / q*B*sqrt(2qV/m)
R=2V/Bsqrt(2qV/m)
At this point I have the radius R of the circular path that the magnetic field induces, but I'm totally lost at this point. I'm assuming it's just geometry of some fashion. Really would appreciate help.