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utkarshakash
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Homework Statement
Three identical metal spheres are uncharged at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the equilateral triangle at its center, see the picture. As a result, the first small sphere acquires charge q1 and second charge q2 (q2 < q1). What is the charge that the third sphere (q3) will acquire?
The Attempt at a Solution
When the first sphere is connected to larger sphere,
charge on bigger sphere = Q-q1
Since the wire is conducting, the potential at the surfaces of bigger and smaller spheres will be the same.
[itex]\dfrac{k(Q-q_1)}{R} = \dfrac{k q_1}{r} \\
Q = q_1 \left( 1+ \frac{1}{\mu} \right) [/itex]
where μ=r/R
Similarly I get the relation q1=q2(1+μ)
Following a similar approach, I get
[itex] q_3 = q_1 - q_2 + \frac{q_2^2}{q_1} [/itex]
But this is not the correct answer.