Phys2212_32.4+to+32.6

Phys2212_32.4+to+32.6 - Physics 2212 Electricity and...

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Physics 2212 Electricity and Magnetism Lecture 19 (Knight: 32.4-32.6) Biot-Savart and Ampere’s Laws
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10/06/09 Physics 2212 - Lecture 19 Magnetic Force A current consists of moving charges. Ampere’s experiment implies that a magnetic field exerts a force on a moving charge. This is true, although the exact form of the force relation was not discovered until later in the 19 th century. The force depends on the relative directions of the magnetic field and the velocity of the moving charge, and is perpendicular to both. . ( 29 F q v B = × r r
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10/06/09 Physics 2212 - Lecture 19 Cyclotron Motion Consider a positive charged particle with mass m and charge q moving at velocity v perpendicular to a uniform magnetic field B . The particle will move in a circular path of radius r cyc because of the force F on the particle, which is: 2 cyc mv F qvB r = = cyc mv r qB = cyc cyc cyc (independent of and ) 2 2 v q B f r v r m π = =
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10/06/09 Physics 2212 - Lecture 19 Example : The Radius of Cyclotron Motion An electron is accelerated from rest through a potential of 500 V, then injected into a uniform magnetic field B. Once in the magnetic field, it completes a half revolution in 2.0 ns. What is the radius of the orbit? 1 2 2 ( ) 0 0 mv e V + - = + 7 2 1.33 10 m/s eV v m = = × 8 cyc 9 1 1 2.5 10 Hz 2(2.0 10 s) f T - = = = × × cyc 3 2 8.94 10 T e mf B π - = = × 3 cyc 8.47 10 m 8.47 mm mv r qB - = = × =
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10/06/09 Physics 2212 - Lecture 19 The Cyclotron Accelerator When a charged particle moves in a uniform field, f cyc is independent of both radius and energy. One can “pump” energy into the particle as it cycles, using an electric field that varies with the frequency f cyc . This is the basic principle of the cyclotron, a particle accelerator that can increase the energies of charged particles. The ultimate energy of a cyclotron is determined by the radius R of the magnet: E max = (RqB) 2 /2m
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10/06/09 Physics 2212 - Lecture 19 Measuring Momentum with Magnetic Deflection* orbit orbit = so mv p r p qBr qB qB = = In other words, by measuring the orbit radius of curvature r orbit of a particle with charge q that is deflected by a uniform perpendicular magnetic field B into a circular orbit, one is measuring the momentum p of the particle.
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This note was uploaded on 06/07/2009 for the course PHYSICS 2212 taught by Professor Geist during the Fall '09 term at Georgia Perimeter.

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Phys2212_32.4+to+32.6 - Physics 2212 Electricity and...

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