Question 99 of 311

Two particles $A$ and $B$ having charges $20\mu C$ and $-5\mu C$ respectively are held fixed with a separation of $5cm$ At what position a third charged particle should be placed so that it does not experience a net electric force ?

AAt $5cm$ from $-5\mu C$ on the right sideBAt $5cm$ from $20\mu C$ on the left side of systemCAt $1.25cm$ from $-5\mu C$ between two chargesDAt midpoint between two charges

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Answer: (A) At $5cm$ from $-5\mu C$ on the right side

Charge should be placed near $-5\mu C$ at $x$ distance

$\dfrac{K(20)Q}{(5+x{)}^{2}}=\dfrac{K(5)Q}{{X}^{2}}$
$4{x}^{2}=(5+x{)}^{2}$
$4{x}^{2}=25+{x}^{2}+10x$
$3{x}^{2}-10x-25=0$ $\Rightarrow x=5$