Two point charges + 9e and + e are at 16 , cm away from each othe… - Vidyadip

MCQ

Two point charges $ + 9e$ and $ + e$ are at $16\, cm$ away from each other. Where should another charge $q$ be placed between them so that the system remains in equilibrium

A
$24\, cm$ from $ + 9e$
✓
$12\, cm$ from $ + 9e$
C
$24\, cm$ from $ + e$
D
$12\, cm$ from $ + e$

✓

Answer

Correct option: B.

$12\, cm$ from $ + 9e$

b
(b) Suppose $q$ is placed at a distance $x$ from $+9e$, then for equilibrium net force on it must be zero i.e. $|F_1| = |F_2|$
Which gives ${x_1} = \frac{x}{{\sqrt {\frac{{{Q_2}}}{{{Q_1}}}} + 1}} = \frac{{16}}{{\sqrt {\frac{e}{{9e}}} + 1}} = 12\,cm$

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