- #1
vladimir69
- 130
- 0
Homework Statement
2 conducting spheres of radius r=0.5cm are connected by a long thin piece of conducting wire of length L=2metres. A charge of 60 micro Coulombs is put onto one of the spheres, find the tension T in the wire. Assume the charge is evenly distributed along the surface of the two spheres.
Homework Equations
[tex]F=k_{e}\frac{Qq}{r^2}[/tex]
[tex]Q=30\mu C[/tex]
Q is 30 micro Coulombs because I assumed that the charge would distribute evenly onto the surface of both spheres.
The Attempt at a Solution
This question was in the Gauss Law chapter of my book however I didn't use Gauss Law for this one.
I said
[tex]F_{12}=k_{e}\frac{Q^2}{L^2}[/tex]
[tex]F_{21}=-F_{12}[/tex]
So according to me each sphere is "pulling" the rope in opposite directions to produce a combined force of
[tex]F=2F_{12}[/tex]
The tension in the wire must balance this force otherwise it will break
So
[tex]F_{wire} = F=4N[/tex]
However the answer gives 2 Newtons which I can't convince myself is right because each sphere is contributing its own force on the string.