How Fast Are Charged Particles Moving When Halfway Together?

[metalmagik]

Homework Statement

Two particles each have a mass of 5.9e-3 kg. One has a charge of +5.0e-6 C, and the other has a charge of -5.0e-6 C. They are initially held at rest at a distance of 0.70 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value?

Homework Equations

$$F = kq1q2/r^2$$

$$E = F/q$$

$$V=Ed$$

$$CV = q$$

$$Energy = 1/2CV^2$$

$$KE = 1/2mv^2$$

The Attempt at a Solution

F = kq1q2/r^2

F = (8.99e9)(5e-6)(5e-6)/.35^2

F = 1.83 N

E = F/q

E = 1.83/5e-6

E = 366,000 N/C

V = Ed

V = (366000)(.35)

V = 128,100 V

q = CV

(5e-6) = (128,100)C

C = 3.90e-11

Energy = 1/2CV^2

Energy = .5(3.9e-11)(128100)^2

Energy = .32 J

KE = 1/2mv^2

.32 = 1/2(5.9e-3)v^2

v = 10.4 m/s

Verification on this would be very greatly appreciated.

 

[OlderDan]

Several of the equations you have written are not relevant to this problem. One key equation you have left out and need to use is the equation for the electrical potential energy of two point charges exerting forces on one another. That energy can be thought of as the potential energy of one charge that finds itself in the electric field produced by another charge. Associated with the vector electric field is a scalar electric potential, which is potential energy per unit charge. What is the electric potential produced by a point charge?