Three charges -q, Q and -q are placed at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q

Question

Three charges -q, Q and -q are placed at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q (A) 1:1 (B) 1:2 (C) 1:3 (D) 1:4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-jxb8jftvuk6vppyx.jpg" /> U=(- k Q q/r)× 2+(k q2/2 r)=0 2× (k Q q/r)=(k q2/2 r) 2× (Q/1)=(q/2) (Q/q)=(1/4)

Q. Three charges $- q, Q$ and $- q$ are placed at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of $Q : q$

$1 : 1$

$1 : 2$

$1 : 3$

$1 : 4$

$U = \frac{- k Qq}{r} \times 2 + \frac{k q ^{2}}{2 r} = 0$
$2 \times \frac{k Qq}{r} = \frac{k q ^{2}}{2 r}$
$2 \times \frac{Q}{1} = \frac{q}{2}$
$\frac{Q}{q} = \frac{1}{4}$

Q. Three charges −q,Q and −q are placed at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q

1:1

1:2

1:3

1:4