A Deflected Charge

A charged particle of charge \(^+\!q\) and mass \(m\) is moving from infinity towards a charge \(^+\!Q\) with a velocity \(v\). The particle is eventually deflected due to the repulsion force in accordance with Coulomb's law.

Given the impact parameter \(b\), find the scattering angle, \(\theta\), in degrees.

Details and Assumptions

  • Assume that this system is in isolated gravity free space.
  • The charge \(^+\!Q\) is fixed.
  • Only Coulombic forces are present.
  • Impact parameter is the distance between the line of incidence and the fixed charge.
  • Scattering angle is the angle made by terminal velocity with initial velocity.
  • Take \(q=1.0\,e \), \(~Q=6.0\,e\), \(m = 1.67\times10^{-26}\text{ kg}\), \(v = 1089\text{ ms}^{-1}, b = 57\text{ nm}\).
  • \(e\) is elementary positive charge.
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