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  4. 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?

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Q. 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?

Electric Charges and Fields

Solution:

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{K e q}{(16-r)^{2}} $
$\Rightarrow \frac{3}{r}=\frac{1}{16-r} \Rightarrow r=12\,cm$