Download 26. Applications of Magnetic Force on Moving Charges

Devices that use magnetic force on a moving charge (22.4)
LORENTZ FORCE: expression for total magnetic and electric force on a charge
• In space containing electric and magnetic field together:
o force on moving charge is
r
r
r r
F = qE + qv × B
(Lorentz Force)
o For special choice of fields & particle velocity, Lorentz force can be zero
ƒ Important for devices used to analyse molecules in chemistry,
physics, biochemistry, medicine, etc.
VELOCITY SELECTOR
• Contains region of space with uniform electric and magnetic fields
o perpendicular to each other
o perpendicular to path of charged particle
Barrier with hole
E (down)
+ + + + + + +
• In selector region:
r
r r
o FB = q v × B is “up” by RHR
r
r
o FE = q E is “down”
• Net force on charge is zero IF
qv B = q E
v
+q
- - - - - - B (into screen)
E
v
=
• So particles with speed
B are undeflected
o Can be directed through hole in barrier to give beam of particles with
same speed regardless of mass and charge (other speeds miss hole)
o Can THEN analyse for charge and mass
MASS SPECTROMETER
• Measures mass/charge (m/q) for ionized molecules and fragments
o Charge of fragment is multiple of e → | q | = e, 2e, 3e K
o Because charge can be inferred, provides measure of mass
• Important in
o analytical & synthetic chemistry (identification of contaminants,
identification of reaction intermediates, etc.)
o health & medicine (genetic sequencing, drug testing, analysis of medical
samples)
o biochemistry (identification of proteins sequences and biological
molecules)
o earth science and material science (mineral and alloy characterization,
etc.)
MASS SPECTROMETER (continued)
• 1st: ionize molecules and fragments and
accelerate (i.e. in electric field)
• 2nd: use velocity selector to pick out
fragments with vs = Es / Bs
o Others hit barrier
Detector
r
v
• 3 : inject ions with speed s into uniform B
with magnitude B0
m vs
=
r
o Radius of path is
q B0
velocity selector
rd
r
Bs, Es
+ + + + + + +
m rBs B0
• SO: q = E
s
vs
v
+q
+q
- - - - - - -
B0
CYCLOTRON – device to accelerate charged particles to high energy
• Potential difference across
gap changes each time
particle reaches gap
Bup
o “kick” raises K by q∆V
r
• for charge q in uniform B
mv
r
=
o found
qB
o period of orbit is: T =
alternating
voltage
source
+q
circumf . 2 π r 2 π m
=
=
v
v
qB
• NOTICE: period does NOT depend on speed
o Can alternate potential difference across gap at constant frequency
ƒ “kick” will occur at correct time each orbit even as speed increases
o Raise K until particle leaves (or relativistic effects become important)
• 1st Cyclotrons used for nuclear physics
o Lawrence in 1931 (less than 11” diameter)
• Also used in nuclear
medicine
o Particle beam
therapies
o Medical isotopes
o Positron emission
tomography
World’s biggest cyclotron –
TRIUMF in Vancouver