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Relativistic Electron Mass

Relativistic Electron Mass. James Durgin April 30, 2009 Physics 521. Overview. Physical Theory Experimental Theory Experimental Design Determining Magnetic Field Determining Electric Field Results/Uncertainty Analysis. Physical Theory.

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Relativistic Electron Mass

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  1. Relativistic Electron Mass James Durgin April 30, 2009 Physics 521

  2. Overview • Physical Theory • Experimental Theory • Experimental Design • Determining Magnetic Field • Determining Electric Field • Results/Uncertainty Analysis

  3. Physical Theory • Particle behavior changes as velocity approaches speed of light • Mass increases as v -> c m =γmo

  4. Experimental Theory • Sr-90, Y-90 emit β-with energies up to 2.820 MeV • Applied magnetic field causes electrons to undergo uniform circular motion • An electric field can balance out the magnetic field by F=q(E+vxB) • Scintillator detects electrons

  5. Experimental Theory

  6. Determining B-field • 4 points measured along path • Standard deviation determines uncertainty • 3rd degree polynomial fit due to hysteresis

  7. B Field (T) Uncertainty 0.00799579 0.001000276 0.0100598 0.00100011 0.01198767 0.00100002 0.01403391 0.001000053 0.01602358 0.001000201 0.01807416 0.001000461 0.01900479 0.002000266 Determining B-field • Uncertainty for calibration points used since similar currents

  8. Determining E-field • 7 applied magnetic fields • 13 applied electric fields centered around peak per magnetic field • Points fit with Gaussian

  9. Fitted Range B Field (T) Uncertainty Fitted Mean (V) Uncertainty X2 Probability 2.90 to 2.55 0.00799579 0.001000276 2734 10 39.08% 4.15 to 3.80 0.0100598 0.00100011 3992 16 7.87% 5.45 to 5.11 0.01198767 0.00100002 5202 21 88.60% 6.80 to 6.30 0.01403391 0.001000053 6528 7 47.68% 8.15 to 7.65 0.01602358 0.001000201 7854 14 18.96% 9.35 to 8.95 0.01807416 0.001000461 9181 19 99.33% 9.95 to 9.60 0.01900479 0.002000266 9801 55 5.26% Determining E-field

  10. Results • Find m and β for each magnetic field • Take partial derivates to find uncertainty • Compare with accepted results • Find e/mo • Take partial derivates to find uncertainty • Compare with accepted result

  11. Results- m v. β

  12. e/m0 Uncertainty B Field (T) -1.69769E+11 2.332E+09 0.00797918 -1.70868E+11 2.337E+09 0.01005596 -1.69562E+11 2.345E+09 0.01198147 -1.68812E+11 2.408E+09 0.01401906 -1.69488E+11 2.748E+09 0.01600245 -1.67587E+11 3.044E+09 0.01805708 -1.67847E+11 3.427E+09 0.01899531 Results- e/mo Experimental: -169.1E9 ± 1.1E9 C/kg Accepted: -176E9 C/kg

  13. Conclusion • Experiment demonstrates relativistic effects • Need to calculate partial derivates for non-linear experiments • Rotated Hall probe likely responsible for increased mass

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