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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 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 “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