How can i find the Potential difference?

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SUMMARY

The discussion focuses on calculating the potential difference required to accelerate an electron from rest to a speed of 0.99c. The relevant equation used is E=γmc²=V*q, where γ represents the Lorentz factor. The initial calculation yielded 3.63e6 eV, but the correct potential difference is 3.1e6 V. The confusion arose from the relationship between energy in electronvolts (eV) and volts (V), clarified by the equation Vg=mc²(γ-1).

PREREQUISITES
  • Understanding of relativistic physics concepts, particularly the Lorentz factor (γ).
  • Familiarity with the relationship between energy, charge, and potential difference.
  • Basic knowledge of electron properties, including mass (9.11e-31 kg) and charge (1.6e-19 C).
  • Proficiency in using energy equations in physics, specifically E=mc².
NEXT STEPS
  • Study the derivation of the Lorentz factor (γ) and its implications in relativistic physics.
  • Explore the relationship between energy in electronvolts and potential difference in volts.
  • Learn about the principles of particle acceleration and the role of electric fields.
  • Investigate advanced topics in electromagnetism related to charged particles in motion.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of particle acceleration and relativistic energy calculations.

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Homework Statement


Through what potential difference must an electron be accelerate, starting from rest, to acquire a speed of 0.99c?

vf=0.99c(m/s), vi=0(m/s), m=9.11e-31(kg), q=1.6e-19(C)

Homework Equations



E=γmc^2=V*q

The Attempt at a Solution


I plugged in all knowns in the equation and find V(emf).

What i got is 3.63e6 eV but the answer is 3.1e6 V.

What did i do wrong in the progress??
 
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The voltage gives the electron extra energy over its rest energy, mc^2. So Vg=mc^2(γ-1).

ehild
 
But how does (γ-1) come from??
 
ehild, Never mind, i got it!

But should the unit be eV rather than V?
 
The question is potential difference, that is volts. But the change of energy of the electron is the same number in eV as the acceleration voltage: 1 elementary charge times U potential difference is 1*U =U eV.

ehild
 

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