What Happens to the Speed and Proximity of Two Charged Metal Spheres in Motion?

[Digdug12]

Homework Statement

A small metal sphere, carrying a net charge of q_1 = -2.60 \mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.70 \mu C and mass 1.40 g, is projected toward q_{1}. When the two spheres are 0.800 \rm m apart, q_{2} is moving toward q_{1} with speed 22.0 \rm m/s . Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.
What is the speed of q_{2} when the spheres are 0.450 m apart
?How close does q_{2} get to q_{1}?

Homework Equations

Ka+Ua=Kb+Ub
U=qv
V=k(q1/r)

The Attempt at a Solution

I figured this was a simple conservation of energy problem, so i began it at such.
.5m2Vi^2 + q2Va = .5m2Vf^2 + q2Vb

after simplifying it all down i got:
sqrt((m2vi^2 + q2(Va-Vb))/m2) = Vf

I calculated Va to be -29233V and Vb to be -51952V. I am not sure what i did wrong here.
to calculate V i used q1, the charge of motionless sphere, since V is independent of the observer charge. For the r i used the distance from the moving sphere to sphere, and i used both values. when multiplying (Va-Vb) by q i used the q value of the moving sphere. Please help!

 

[Doc Al]

What's the electrical potential energy between two point charges?

 

[tomcue]

Your approach of using conservation of energy is correct. However, you have made a mistake in calculating the initial and final potential energies. The potential energy formula, U=qV, should be used to calculate the potential energy of each sphere, not the velocity. Additionally, you need to use the distance between the two spheres at each position, not just the distance from the moving sphere to the stationary one. The correct formula to use is V=k(q1/r1 + q2/r2), where r1 is the distance between the stationary sphere and the point where you want to calculate potential energy, and r2 is the distance between the moving sphere and the same point. Once you have the correct values for potential energy, you can proceed with your conservation of energy equation. Remember to use the correct units for all quantities.

To answer the first question, the speed of q2 when the spheres are 0.450 m apart can be calculated using the same equation you used, but with the new values for potential energy and the new distance between the spheres.

For the second question, you can use the equation for the minimum distance between two point charges, r = q1q2/4πε0(Ka+Kb), where Ka and Kb are the initial and final kinetic energies, respectively. Again, make sure to use the correct units for all quantities.