What is the Distance of Closest Approach Between Two Point Charges?

[purduegirl]

Homework Statement

Distance of Closest Approach
Use the similarity between Coulomb's Law and the Law of Universal Gravitation to calculate the distance of closest approach between a point charge of +3.40 × 10-6 C, which starts at infinity with kinetic energy of 8.70 J, and a fixed point charge of +1.15 × 10-4 C. Assume that the moving charge is aimed straight at the fixed point charge.

 

[Dick]

Just use conservation of energy. What's KE+PE at infinity? At closest approach, KE=0, since the point charge has stopped. But the total energy hasn't changed, right?

 

[matthew1991]

I don't understand. Initially total energy and ending with total potential correct? How is this solved?

 

[cupid.callin]

take the two point charges as system! now all the Columbian and gravitational forces are internal forces and hence mechanical energy is conserved.

just use KE_initial + PE_initial = KE_final + PE_final

find PE_final and use it to find the distance at that time

 

[matthew1991]

Okay, i knew total energy is conserved. for anyone who needs it in the future, the closest distance of approach is when all kinetic energy is converted to potential energy. the problem can be solved using this equation: U = K*[q*q/r] where U = potential energy, K = coulomb's constant (8.9875E9), the q's are the respective charges of the particles, and r = distance of closest approach.
Notice that it is just r instead of r squared. this is enegry instead of charge force.

 

[planauts]

Is the answer to this problem 0.404 m? Thanks