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Exploring Momentum, Mass, and Energy in Charged Particle Physics

This comprehensive guide covers the measurement of masses and momenta of charged particles, focusing on momentum in the context of special relativity and kinetic energy in accelerators. It explains the relationship between force, mass, and velocity within magnetic fields using Lorentz force and centripetal force principles. The importance of redefining momentum for conservation purposes is highlighted, as well as the significance of work-energy principles. Through practical examples and exercises, this resource offers insights into experimental methods for identifying particle masses.

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Exploring Momentum, Mass, and Energy in Charged Particle Physics

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Presentation Transcript

  1. Measuring masses and momenta • Measuring charged particle momenta. • Momentum and Special Relativity. • Kinetic energy in a simple accelerator. • Total energy, mass and momentum. • Measuring masses.

  2. v B-field F Motion of Charged Particle in a Magnetic Field • Charge Q, magnetic field strength B. • Velocity v, normal to magnetic field. • Lorentz force F, normal to directions of B and v. • Magnitude of force • Circular path.

  3. Measuring momentum • Centripetal force • Equate Lorentz and centripetal forces

  4. electron momentum (kg m/s) electron velocity (1/c) Momentum and Special Relativity • Measurementof momentumagainst speedfor an electron • Must redefine momentum to keep conservation of momentum • Relativistic momentum:

  5. Kinetic energy in a simple accelerator • Remember two rules: • Work done = _____ x ________. • Change in K.E. = work done. • Build an accelerator to check this: electron gun accelerator plates velocity measurement

  6. v2 (1/c2) work done (mc2) Kinetic energy cont. • More measurements: • If want to keep K.E. = work done, define: where

  7. Energy and mass • Have seen:so know E = mc2 (ignoring K.E.). • Putting it all together: • Rememberingcan show that and

  8. An aside, units • We have • Multiply p by c to get energyBut Q = 1.6x10-19 C for e,  etc. • Now c = 3x108 ms-1 so: • Finally, express p in units of GeV/ c:

  9. PC Exercise 2 • Use PC to do following experiment: Side viewEnd view +, +, K+ or p E known e+ e- B field -, -, K- or p +, +, K+ or p Measure r, hence get p -, -, K- or p

  10. PC exercise 2 cont. • Using known energy (from energy conservation) and momentum (from r measurement) calculate mass: • Compare with known particle masses, can you identify the particles?

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