Question

Two-point charges $Q_1$ and $Q_2$ are $3\text{m}$ apart and their combined charge is $20\mu \text{C}$. If one repels the other with force of $0.075\text{N}$. Calculate the two charges. (in $\mu \text{C}$)

• A. $10,10$
• B. $15,5$
• C. $35,-15$
• D. $25,-5$

Answer 1

The correct option is B $15,5$

Given that,
Separation between the charges, $r=3\text{m}$
$Q_1+Q_2=20\mu \text{C}\dots \dots \left(1\right)$
The force is repulsive, so according to Coulomb's law
$0.075=\frac{1}{4\pi {ϵ}_0}\frac{Q_1{Q}_2}{r^2}$
$\Rightarrow 0.075=9\times {10}^9\left[\frac{Q_1{Q}_2}{(3{)}^2}\right]$

$Q_1{Q}_2=75\times {10}^{-12}{\text{C}}^2=75(\mu \text{C}{)}^2$
Substituting value of $Q_2$ from equation $\left(1\right)$
$Q_1(20-Q_1)=75$
$\Rightarrow Q_1^2-20Q_1+75=0$
$\Rightarrow Q_1^2-5Q_1-15Q_1+75=0$
$\Rightarrow Q_1(Q_1-5)-15(Q_1-5))$
$\Rightarrow (Q_1-5)(Q_1-15)$
$\Rightarrow Q_1=5$ and $15$
So, $Q$'s are $5\mu \text{C}$ and $15\mu \text{C}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: Like charges attracts and unlike}\\ \text{charges repel each other. You can}\\ \text{eliminate the option (c) and (d) by}\\ \text{just looking at the sign of charges.}\end{array}$