Two point charges +9 e and +e are kept 16 cm apart from each other. Where should a third charge q be placed between them so that the system is in equilibrium state?

Question

Two point charges +9 e and +e are kept 16 cm apart from each other. Where should a third charge q be placed between them so that the system is in equilibrium state? (A) 24 cm from +9e (B) 12 cm from +9e (C) 24 cm from +e (D) 12 cm from +e

Tardigrade Admin · Accepted Answer

Let the charge q be placed between the given two charges and at a distance r from the charge 9 e. (K(9 e) q/r2)=(K e q/(16-r)2) ⇒ (3/r)=(1/16-r) ⇒ r=12 cm

Q. Two point charges $+ 9 e$ and $+ e$ are kept $16 c m$ apart from each other. Where should a third charge $q$ be placed between them so that the system is in equilibrium state?

24 cm from +9e

12 cm from +9e

24 cm from +e

12 cm from +e

Let the charge $q$ be placed between the given two charges and at a distance $r$ from the charge $9 e$ .
$\frac{K ( 9 e ) q}{r ^{2}} = \frac{Ke q}{( 16 - r ) ^{2}}$
$\Rightarrow \frac{3}{r} = \frac{1}{16 - r} \Rightarrow r = 12 c m$

Q. Two point charges +9e and +e are kept 16cm apart from each other. Where should a third charge q be placed between them so that the system is in equilibrium state?