PARTICLE MOTION IN MAGNETIC FIELDS
Newton’s 2nd Law:
F = qvB = mv2/R
Particle moves in a circular orbit of radius R with the constant speed v
Radius of orbit
R = mv/qB
(unit: m)
Period of orbit
T = 2πR/v = 2πm/qB (unit: s) --- time for one orbit
Frequency of orbit
f = 1/T = qB/2πm (unit: s-1 or Hz) --- # of revs per sec
Angular frequency
ω = 2πf = qB/m (unit: rad/s or s-1)
More generally, a particle can move in a helical orbit whose axis is along a magnetic
field line (e.g. van Allen belts, magnetic bottle)
MASS SPECTROMETER
R = mv/qB
implies that
m = qBR/v
Make q = +e (by ionizing the atom)
Choose v by accelerating the ion through a potential difference
Pass ion through magnetic field B and measure radius of path R
Then use above equation to calculate m from q,v,B and R.
VELOCITY SELECTOR
E = Electric Field B = Magnetic Field
V = E/B = velocity of particles that pass undeflected through selector
Doesn’t depend on mass or charge of particles!!
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