Two charges 4q and q are placed at distance l . In the middle adjoining line a charge Q is kept. If resultant force on q will be zero, then Q will be

Question

Two charges 4q and q are placed at distance l . In the middle adjoining line a charge Q is kept. If resultant force on q will be zero, then Q will be (A)  +q  (B)  -q  (C)  +2q  (D)  -2g

Tardigrade Admin · Accepted Answer

Here FAB+FCB=0 (1/4π ε 0).(4q2/l2)+(1/4π ε 0).(Qq/l2/4)=0 ⇒ 4Qq=-4q2 ⇒ Q=-q

Q. Two charges $4 q$ and $q$ are placed at distance $l$ . In the middle adjoining line a charge $Q$ is kept. If resultant force on $q$ will be zero, then $Q$ will be

$+ q$

$- q$

$+ 2 q$

$- 2 g$

Here $F_{A B} + F_{CB} = 0$
$\frac{1}{4 π ε _{0}} . \frac{4 q ^{2}}{l ^{2}} + \frac{1}{4 π ε _{0}} . \frac{Qq}{l ^{2} /4} = 0$
$\Rightarrow$ $4 Qq = - 4 q^{2}$
$\Rightarrow$ $Q = - q$

Q. Two charges 4q and q are placed at distance l . In the middle adjoining line a charge Q is kept. If resultant force on q will be zero, then Q will be

+q

−q

+2q

−2g