- #1
slugbunny
- 15
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Homework Statement
Two identical spheres with mass m are hung from silk thread with length L. Each sphere has the same charge, so q1=q2=q. The radius of each sphere is very small compared to the distance between the two spheres, so they may be treated as point charges. Show that if the angle θ is small, the equilibrium separation d between the spheres is
d=(q2L/2πε0mg)1/3
(Hint: If θ is small, tanθ=sinθ)
Homework Equations
F=ma=Eq
The masses are hung from thread connected at the same point so that it looks pendulum-esque and possible use of triangles.
The Attempt at a Solution
Well I started off with this equation
F=mg=Eq
then used symmetry
mg=2Exq
mg=2E sin(θ) q
mg=2q/(4πε0) (1/(1/2d)2) sin(θ) q
and sin(θ)=r/L so I got
mg=2q2/(4πε0) (4/d2) (r/L)
mg=2q2/(πε0d2) (d/2L)
mg=q2/(πε0dL)
and d is...
d=q2/(πε0Lmg)
I'm thinking that I would get the correct d if I lose the 2 from the electric field symmetry and switch the sin(θ) values (L/r instead of r/L), then I would get a d3 and an L in the numerator and it would work fine hahaha.
Thanks for help!