PHYSICS 7D Study Guide - Quiz Guide: Centripetal Force
Physics 7D Quiz 5
Name: Jordan Smolinsky
A muon is basically a heavier electron. While the electron weighs 9.11 ×10−31 kg the
muon weighs a whopping 1.88 ×10−28 kg, but they both have the same charge. Suppose
that an electron and a muon enter the same magnetic field with the same kinetic energy.
The electron moves in a circular path with radius of curvature 1 m. What is the radius of
curvature of the muon’s path?
Solution
When a charged particle enters a magnetic field it is subject to a magnetic force
~
FB=q~v ×~
B(1)
Because this force is always perpendicular to the velocity the particle will move in a
circular orbit. Whenever a body executes a circular trajectory we can write the centripetal
force keeping it on that trajectory as
FC=mv2
r(2)
where ris the radius of the circular path. The radius of curvature of a charged particle
orbit in a magnetic field is then given by
r=mv
qB (3)
Because the electron and muon have different masses but the same kinetic energy, we
know that
1
2mµv2
µ=1
2mev2
e
⇒vµ
ve
=rme
mµ
(4)
so we can write the ratio of their radii of curvature as
rµ
re
=mµvµ
meve
=rmµ
me
≈14.37 (5)
so that the muon’s radius of curvature is simply 14.37 m.
1
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PHYSICS 7D Full Course Notes
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Document Summary
While the electron weighs 9. 11 10 31 kg the muon weighs a whopping 1. 88 10 28 kg, but they both have the same charge. Suppose that an electron and a muon enter the same magnetic eld with the same kinetic energy. When a charged particle enters a magnetic eld it is subject to a magnetic force (cid:126)fb = q(cid:126)v (cid:126)b (1) Because this force is always perpendicular to the velocity the particle will move in a circular orbit. Whenever a body executes a circular trajectory we can write the centripetal force keeping it on that trajectory as where r is the radius of the circular path. The radius of curvature of a charged particle orbit in a magnetic eld is then given by. Because the electron and muon have di erent masses but the same kinetic energy, we know that r = mv qb (3) so we can write the ratio of their radii of curvature as.
