Two Insulating Spheres in Each Other's Electric Field

by faceoclock
Tags: electric, field, insulating, spheres
 P: 5 Hi, I'd like to ask the good people of this forum for some help. Here's a problem I've been working on for a while, and I'm seriously at my wit's end. I guess there's something I'm missing here... 1. The problem statement, all variables and given/known data Two insulating spheres have radii r1 and r2, masses m1 and m2, and uniformly distributed charges -q1 and q2. They are released from rest when their centers are separated by a distance d. How fast is each moving when they collide? Suggestion: Consider conservation of energy and of linear momentum. 2. Relevant equations I thought these were relevant: Momentum=mv Kinetic energy = 1/2(mv^2) $$\Delta$$U = -q$$\int$$E dr 3. The attempt at a solution First I solved for the potential energy that this system gains when the two spheres are moved apart: $$\Delta$$U = q1$$\int^{d}_{d-r1-r2}$$E dr = k(q1)(q2)($$\frac{1}{d-r1-r2}$$ - 1/d) I figured this is the amount of energy the spheres would have when they collide, so... $$\Delta$$U = $$\frac{1}{2}$$(m1)v$$^{2}_{1}$$ + $$\frac{1}{2}$$(m2)v$$^{2}_{2}$$ From conservation of momentum, v2 = (m1/m2)v1 so subbing that into the above equation I got: $$\Delta$$U = $$\frac{1}{2}$$m1v$$^{2}_{1}$$ + $$\frac{1}{2}$$$$\frac{m^{2}_{1}}{m_{2}}$$v$$^{2}_{1}$$ So then I solved for v1 to get: v1 = $$\sqrt{\frac{2kq_{1}q_{2}((1/(d-r1-r2)-(1/d))}{m_{1}+\frac{m^{2}_{1}}{m_{2}}}}$$ And v2 can be figured out the same way. However, I know for a fact this isn't the right answer. In closing I'm don't really know what I did wrong, but I suspect it's because I treated the two spheres as point charges, and I'm not sure if I'm justified in doing that.