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Homework Statement
We have a uniformly charged, non-conducting sphere (charge per volume,ρ, and radius, R). Then a uniformly charged ruler (charge per length,λ, and length, d) is aligned radially almost touching the surface of the sphere. Determine the net force experienced by the ruler.
Homework Equations
∫E⋅dA=Qenclosed/ε0
I think that's all...
The Attempt at a Solution
I drew my gaussian surface like Gaussian surface.jpg
∫E⋅dA=Qenclosed/ε0
ρ=(Q/V)=Q/(4/3)πR2→Q=ρ(4/3)πR2
A=4πR12
∫E⋅dA=Qenclosed/ε0→E4πR12=ρ(4/3)πR2/ε0
E=ρR2/3ε0R12
Now I have the electric field of the sphere at its surface
When I place a ruler almost touching the sphere aligned radially I am not sure what to do... The ruler also has an electric field which we could calculate using gauss's law (the shape would be a box?). I know the spheres electric field interacts with the charged ruler...
Any help would be appreciated!