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Potential energy

A charged particle q is shot towards another charged particle Q which is fixed, with a speed  ν. It approaches Q upto a closest distance r and then returns. If q were given a speed  2ν , the closest distances of approach would be


Charge q will momentarily come to rest at a distance r from charge Q when all it's kinetic energy converted to potential energy i.e.  12mv2=14πε0.qQr
Therefore the distance of closest approach is given by  r=qQ4πε0.2mv2r1v2

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