# 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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