(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two identical spheres with massmare hung from silk thread with lengthL. Each sphere has the same charge, soq. 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_{1}=q_{2}=qθis small, the equilibrium separation d between the spheres is

d=(q^{2}L/2πε_{0}mg)^{1/3}

(Hint: Ifθis small, tanθ=sinθ)

2. Relevant 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.

3. The attempt at a solution

Well I started off with this equation

F=mg=Eq

then used symmetry

mg=2E_{x}q

mg=2E sin(θ) q

mg=2q/(4πε_{0}) (1/(1/2d)^{2}) sin(θ) q

and sin(θ)=r/L so I got

mg=2q^{2}/(4πε_{0}) (4/d^{2}) (r/L)

mg=2q^{2}/(πε_{0}d^{2}) (d/2L)

mg=q^{2}/(πε_{0}dL)

and d is...

d=q^{2}/(πε_{0}Lmg)

I'm thinking that I would get the correctdif 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 d^{3}and an L in the numerator and it would work fine hahaha.

Thanks for help!

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# Homework Help: Electric force between two point charges

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