Register to reply

Two Insulating Spheres in Each Other's Electric Field

by faceoclock
Tags: electric, field, insulating, spheres
Share this thread:
Oct12-08, 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 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:
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}_{d-r1-r2}[/tex]E dr = k(q1)(q2)([tex]\frac{1}{d-r1-r2}[/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/(d-r1-r2)-(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.
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Oct13-08, 12:17 AM
P: 5
Question was solved. Thanks a lot to everyone who took the time to read this :P

Register to reply

Related Discussions
Insulating Spheres in Electric Fields Introductory Physics Homework 2
Gauss' Law: Net Electric Field of Two Spheres Advanced Physics Homework 3
Electric field within a very large, charged, insulating slab? Advanced Physics Homework 5
Two small insulating spheres with radius Introductory Physics Homework 2
Electric field from concentric spheres Introductory Physics Homework 4