A Deflected Charge

Classical Mechanics Level 5

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

If the impact parameter (the distance between the line of incidence and the charge) is \(b\) and \(\theta\) is the scattering angle (the angle made by terminal velocity vector with initial velocity vector), find \(\theta\) in degrees.

Details and Assumptions

  • The charge \(^+\!Q\) is fixed and does not move due to Coulomb's force.
  • The repulsion force from Coulomb's law is the only force present.
  • 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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