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Hov
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Homework Statement
"Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium they are a distance R apart. Determine the charge on each bead. (Use k_e for ke, g for the acceleration due to gravity, m, and R as necessary.)"
Here's a picture:
http://img3.imageshack.us/i/p2368.gif
Homework Equations
Relevant equations include Coulomb's Law, and other elementary physics equations.
F = Ke * (q1) * (q2) / (distance)2
Where Ke = 8.9 x 109
The Attempt at a Solution
So what I've gotten so far is this:
Using the left-most ball as a model, there's a force in the negative x direction from the ball on the right. That force is exactly
F = -Ke * (qe)2/R2
Now there's a y component of the normal force from the hemisphere given by:
mgsin(x) = N
So, I also figured that the normal and the gravitational forces should each have an x component and that it should be equal and opposite of the force from the charge on the right:
Ncos(x) = Force from the charge
So here's what I did from there:
Ncos(x) = Ke * (qe)2/R2
Nsin(x) = mg
tan(x) = mg / ( Ke * (qe)2/R2 )
R2 / tan(x)mg = Ke * (qe)2
R2 / tan(x)mg * Ke = (qe)2
And ended up with:
qe = sqrt ( R2 / tan(x)mg * Ke )
Which is incorrect.
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