# 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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