Three charges + q , − q , + q are placed randomly along a straight line at points P 1 , P 2 , P 3 . The potential energy of this system of charges is u 1 when -q charge is in the middle and is

Question

Three charges + q , − q , + q are placed randomly along a straight line at points P 1 ​ , P 2 ​ , P 3 ​ . The potential energy of this system of charges is u 1 ​ when -q charge is in the middle and is u 2 ​ when -q charge is at one end. Then ratio u 2 ​ u 1 ​ ​ is equal to :-

TestHub · Accepted Answer

Points are equally spaced by a. With -q in the middle: $u_{1} = - \frac{k q ^{2}}{a} - \frac{k q ^{2}}{a} + \frac{k q ^{2}}{2 a} = - \frac{3 k q ^{2}}{2 a}$ .

With -q at one end: $u_{2} = - \frac{k q ^{2}}{a} + \frac{k q ^{2}}{a} - \frac{k q ^{2}}{2 a} = - \frac{k q ^{2}}{2 a}$ .

$\frac{u _{1}}{u _{2}} = 3$ . Answer: A

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