Two small metallic spheres each of mass m = 0.200 g are suspended as pendulums by light strings of length L shown. The spheres are given the same electric charge of 7.2 nC, and they come to equilibrium when each string is at an angle θ = 5.00o with the vertical. How long are the strings?
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Expert's answer
2020-09-06T17:15:51-0400
Let y-axis be directed upwards and x-axis be directed from 1 charge to 2 charge. Let us determine the forces acting on the each charge.
y-axis: mg−Tcosθ=0 , so T=cosθmg .
x-axis: Tsinθ−Fe=0.
Here Fe is the electrical force between two charges. The distance between charges is 2Lsinθ, so Fe=k(2Lsinθ)2q2 , from x-axis Fe=Tsinθ=mgtanθ.
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