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Last modified: January 26, 2018
Cyclotron Resonance
-------------------
. = magnetic field
. . . . . . y
m --->v |
. . . . . . +--- x
/
. . . . . . z
B is in z direction
Fmag = q(v x B)
If q is +ve then, according to RHR, F is downwards (-y). This will
cause the charge to start moving in a circular fashion. Thus,
Fcentripetal = mv2/r
q(v x B) = qvBsinθ = mv2/r
qB = mv/r
v = qBr/m
ω = qB/m since v = rω
If particle is also moving in the z direction then the motion of the
particle will be a helix. There will be no influence in the z direction
since θ = sinθ = 0.
Velocity Detector
-----------------
B ^ ^ E and FE
| /
|/
+---> v
/
FB
For 0 deflection FE = FB
qE = qvB
Thus, v = E/B