# Electrical Potential Differences Created by Point Charges

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A charge of -2.86 μC is fixed in place. From a horizontaldistance of 0.0580 m, a particle of mass 7.69 x 10-3 kgand charge -8.01 μC is fired with an initial speed of 71.2 m/sdirectly toward the fixed charge. What is the distance of closestapproach?

I was given a work through with the answer of:
ResponseDetails:
Given  q = -2.45 * 10 ^ -6 C
mass   m = 7.49* 10 ^ -3 kg
q ' = -9.86 * 10 ^ -6 C
Speed  v = 85 m / s
Let the distance of the closest approach be r
At closest distance potential energy =  kineticenergy
K q q ' / r  = ( 1/ 2) m v ^ 2
r = 2Kqq' / m v ^ 2
where  K = coulomb constant = 8.99 * 10 ^ 9 N m ^ 2 / C ^2
plug the values    r = 2( 8.99*10 ^ 9 ) ( 2.45*10 ^ -6 ) ( 9.86* 10 ^ -6 ) / [ 7.49* 10 ^ -3 * (85 ^ 2 ) ]
= 8.026 * 10 ^ -3 m
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