Three charges q, 2q and q are to be placed on a straight wire of length 10 m. Determine the positions where the charges should to be placed so that the electrostatic potential energy of the system is a minimum.
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The potential of Infinity is 0. It make in Since it make to answer 2q and 3q charges are at the opposite end of the line.
Therefore if the q charge were not included, this would be the minimum potential energy positions, and switching the q charge with either of the larger charges would only increase the potential energy.
U=K(2q²/r+3q²/10-r+6q²/10)
We can minimise the charge by the derivative with respect to the r=0,
0=kq²(-2\r²+3\(10-r)²
r²/2=(10-r)²/3
Moreover, They are having only interested in the given solutions which lies along the 9cm line
So r=10(6–√−2), To the indeed on the line and fulfils our intuition that the q charge should be closer to the 2q charge than the 3q charge.
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