A charge ' q ' is placed at the centre of the line joining two equal charges ' Q ' The system of the three charges will be in equilibrium, if ' q ' is equal to

Question

A charge ' q ' is placed at the centre of the line joining two equal charges ' Q ' The system of the three charges will be in equilibrium, if ' q ' is equal to (A) -(Q/2) (B) -( Q /4) (C) +( Q /4) (D) +( Q /2)

Tardigrade Admin · Accepted Answer

Consider forces on charge at ' B ' <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ab348a8e3339f6a0ff052981edd64248-.png" /> For equilibrium, F text net =0 FA+Fc=0 (1/4 π G0) (Q2/x2)+(1/4 π G0) (q Q/x2 / 4)=0 Q+4 q=0 ∴ q=-(Q/4)

Q. A charge ' $q$ ' is placed at the centre of the line joining two equal charges ' $Q$ ' The system of the three charges will be in equilibrium, if ' $q$ ' is equal to

$- \frac{Q}{2}$

$- \frac{Q}{4}$

$+ \frac{Q}{4}$

$+ \frac{Q}{2}$

Consider forces on charge at ' $B$ '

For equilibrium, $F_{net} = 0$
$F_{A} + F_{c} = 0$
$\frac{1}{4 π G _{0}} \frac{Q ^{2}}{x ^{2}} + \frac{1}{4 π G _{0}} \frac{qQ}{x ^{2} /4} = 0$
$Q + 4 q = 0$
$∴ q = - \frac{Q}{4}$

Q. A charge ' q ' is placed at the centre of the line joining two equal charges ' Q ' The system of the three charges will be in equilibrium, if ' q ' is equal to

−2Q​

−4Q​

+4Q​

+2Q​