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Question

(a) Suppose the balls having charges $Q_1$ and $Q_2$ respectively.
Initially : $(i)$
Finally : $(ii)$
$F' = \frac{{k\,{{\left( {\frac{{{Q_1} +

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(a) Suppose the balls having charges $Q_1$ and $Q_2$ respectively.
Initially : $(i)$
Finally : $(ii)$
$F' = \frac{{k\,{{\left( {\frac{{{Q_1} + {Q_2}}}{2}} \right)}^2}}}{{{{\left( {\frac{r}{2}} \right)}^2}}} = \frac{{k{{({Q_1} + {Q_2})}^2}}}{{{r^2}}}$
It is given that $F' = 4.5\,F$ so $\frac{{k\,{{({Q_1} + {Q_2})}^2}}}{{{r^2}}} = 4.5\,k.\frac{{{Q_1}{Q_2}}}{{{r^2}}}$
$==>$ ${({Q_1} + {Q_2})^2} = 4.5\,{Q_1}{Q_2}$. On solving it gives $\frac{{{Q_1}}}{{{Q_2}}} = \frac{2}{1}.$

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