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Two Insulating Spheres in Each Other's Electric Field 
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#1
Oct1208, 11:30 PM

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 r_{1} and r_{2}, masses m_{1} and m_{2}, and uniformly distributed charges q_{1} and q_{2}. 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) [tex]\Delta[/tex]U = q[tex]\int[/tex]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: [tex]\Delta[/tex]U = q1[tex]\int^{d}_{dr1r2}[/tex]E dr = k(q1)(q2)([tex]\frac{1}{dr1r2}[/tex]  1/d) I figured this is the amount of energy the spheres would have when they collide, so... [tex]\Delta[/tex]U = [tex]\frac{1}{2}[/tex](m1)v[tex]^{2}_{1}[/tex] + [tex]\frac{1}{2}[/tex](m2)v[tex]^{2}_{2}[/tex] From conservation of momentum, v2 = (m1/m2)v1 so subbing that into the above equation I got: [tex]\Delta[/tex]U = [tex]\frac{1}{2}[/tex]m1v[tex]^{2}_{1}[/tex] + [tex]\frac{1}{2}[/tex][tex]\frac{m^{2}_{1}}{m_{2}}[/tex]v[tex]^{2}_{1}[/tex] So then I solved for v1 to get: v1 = [tex]\sqrt{\frac{2kq_{1}q_{2}((1/(dr1r2)(1/d))}{m_{1}+\frac{m^{2}_{1}}{m_{2}}}}[/tex] 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. 


#2
Oct1308, 12:17 AM

P: 5

Question was solved. Thanks a lot to everyone who took the time to read this :P



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