Charged particle motion in a constant B field - velocity ...

1 X X X X X Suppose we have a magnetic field given by anda particle starts out at the origin moving in the +x particle will move in a circle with the radius R and angularvelocity : zBB 0 =rRvmqvBamF2===rrqBmvR=mqBRv== R Charged particle motion in a constant B field - velocity in plane to forceprovidescentripedalforceindependent of r and X X X X X X X X X X X X X X X X X X X FReview of Circular MotionIf the force F is perpendicular to the velocity , the particle experiences circular motion :RmvamF2==rrRvFForce F is always perpendicular to does no :In an experiment with cosmic rays, a vertical beam of particles that have a charge magnitude of 3e and a mass 12 times the proton mass enters a uniform horizontal magnetic field of and is bent in a semicircle of 95cm.

2 Find the speed of the particle . Is charge positive or negative? ) )( () (12) (362719==== motion in a constant magnetic fieldIf the velocity of the charge particle is perpendicular to the B fieldthe motion is circle with radius R=mv/qB. If the velocity is not perpendicular, the motion is a helix. In thiscase we break up the velocity into components perpendicular v and parallel to the field v||. Therefore have uniformmotion in B looks like extended spring,v|| constant along the Bdirection and v movesin a circle. R (of helix) = mv /qB0= =BvqFrrrElectric/ magnetic velocity SelectorA Charged particle enters a region with perpendicularelectric and magnetic fields. The electric and magnetic forces will cancel if the velocity isjust right. particles with this velocity will go throughundeflected. Others will be = ==1sinBvqBvqEqrrrrr== BEvrrr=Choosing a particular E/B ratio will select the desiredvelocity.

3 Example, E=1,000V/m and B= v = 1,000,000 m/sApplicationsMass Spectrometer (Chemistry)Measure m to identify substances:1.) Ionize atoms by hitting them withaccelerated ) Acelerate ions through known potential if singly ) velocity ) Pass ions through known B field andmeasure '21';''22222222=====Mass Spectrometer (Chemistry)Applications: Paleoceanography: Determine relative abundances of isotopes(they decay at different rates geological age)Space exploration: Determine what s on the moon, Mars, chemical and biol. weapons (nerve gas, anthrax, etc.).Yet another example Measuring curvature of Charged particle in magnetic field is usual method for determining momentum of particle in modern experiments: view: Binto screene+e-B+ Charged particle - Charged particleqBpqBmvR==Thompson s charge/mass ratio of electron measurement22222221 VBEmemeVvBEmeVveVmv=====Found single value of e/mindependent of cathode material.

4 This led to discovery of = x 1011 C/kgNobel prize in 1906 Accelerates protons and deuterons to high energies to bombard atomic : study of nuclear physics. production of radioactive isotopes cancer are thousands of cyclotrons in , the first Atom Smasher E. O. Lawrence and M. S. Livingston , invented particle accelerator, called cyclotron. Won 1939 NobelPrize. CyclotronErnest Lawrence, South Dakota, 1922 Led to giant accelerators near cyclotronCyclotronmqBTfmqB 21;===2max222maxmaxmaxmax221 RmBqmvKmqBRv===Very important to operation of cyclotron frequency of electric fielddoes NOT depend on energy determined bysize of cyclotron. Limit imposedby size and cost of causes particles to move in a circle .Oscillating voltage between Dees accelerates particleseach time particle crosses force on current carrying wireqFSuppose we have a straight wire with current where charges q are moving upwards and there is a B field pointing into this slide.

5 There is a force tending to push the wire to the that current is I = n q v A (Y&F eqn ) withn=#charge/vol, v= velocity and A=area. In a length, L,the #charges = n L A, so the total force magnitude is,If we consider a small line segment, dl, we can writethe vector force eqn. as, BvqFrrr =AILBLBA nqvqvBAnLF===)()(BlIdFdrrr =vLMore Gun ExampleSuppose we have a movable projectile between bars supplying currentflow and a uniform perpendicular magnetic field . Assume, B=4T, I=5000A, projectile width=10cm and mass of bar= ) What is the force on the projectile?B) How fast will be the be moving after it moves a distance 1m?