Wednesday, December 19, 2012
Cyclotron Motion
Cyclotron Motion
A particle moving perpendicular to a constant
magnetic field undergoes uniform circular motion at constant speed, v.
Thus, the magnetic force due to the external
field produces a centripetal
acceleration.
Fmag = qvB = mac
Fmag =
m(v2/r)
Since cyclotron motion occurs when particle
is traveling perpendicular to field:
qvB = mv2/r
rcyc = mv/qB
rcyc = mv/qB
From this expression it is possible to obtain
the charge to mass ratio, which is the topic of Friday’s lab:
q/m
= v/rcyc B
rcyc = mv/qB
In practical applications, B can be set to an appropriate value. The particle speed can be controlled by use
of a known ∆V, to accelerate the particle.
Ampere's Law
Ampere’s
Law
Whenever a total
current I passes through an
area bounded by a closed
curve, the above relationship is
true. This is called Ampere’s Law.
Use the right hand
rule: Point curled fingers in direction
of integration (your choice,
usually!). Thumb pointing up shows
direction of “positive” current.
Diagram shows into
the page as being positive.
Magnetic Force on a moving charge due to an external B
field
•A moving charge is a magnet.
•It alters the space around it, producing a
magnetic field.
• In the presence of an external magnetic field, the charge will experience a
force and change its speed/direction.
Magnetic Force on a moving charge due to an external B
field
Fq = qv X B
= qvBsinα
(direction given by right
hand rule, units of Newtons)
•Only
a moving charge experiences a force.
•There
must be a component of velocity perpendicular to the external field, or
F = 0.
•The
force is mutually perpendicular to v and B.
•The
force on a negative moving charge is in the opposite direction to v X B (left hand rule!)
And did I mention the
Force was due to an external B field???
•Recall that a force is an interaction between two
objects
•A charge cannot experience a force from its
own magnetic field
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