potential = 0(adsbygoogle = window.adsbygoogle || []).push({});

particle of mass m charge q is projected with kinetic energy K at a nucleus mass M charge Q that is at rest. it is shot with 'perfect aim' (along the x axis).

find the distance x to the nucleus when dx/dt of particle is zero.

i know that F = dK/dt = cqQ/x^2 where c = 1/4pi(epsillon naught)

.5m(d/dt)v^2 = cqQ/x^2 (1)

the coulomb force is position dependent force, so:

.5m(dv^2/dx)(dx/dt) = cqQ/x^2 (2)

.5m(dv^3) = cqQ(dx/x^2) (3)

this doesn't make any sense to me. it makes more sense to take the time derivative in (1) just giving Newtons 2nd, and then doing the position dependence.

ma = cqQ/x^2

mvdv = cqQ(dx/x^2)

.5mv^2 = -cqQ/x

and then ?????

i got nothing. any suggestions, clarifications or anything of the like would be much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electrostatics problem

**Physics Forums | Science Articles, Homework Help, Discussion**