Question

The sum of two point charges is $7\mu C$. They repel each other with a force of 1 N when kept 30 cm apart in free space. Calculate the value of each charge.

• A. $2\mu Cand4\mu C$
• B. $2\mu Cand5\mu C$
• C. $9\mu Cand5\mu C$
• D. $4\mu Cand7\mu C$

Answer 1

The correct option is B $2\mu Cand5\mu C$

$\text{Step 1: Force between two charges}$

Given, $F=1N,$ Separation between the charges $r=0.3m$

Let one of two charges $=x\mu C$
Therefore other charge $=(7-x)\mu C$
By Coulomb's law

$F=\frac{k{q}_1{q}_2}{r^2}$

$1N=\frac{9\times {10}^9\times (x\times {10}^{-6}C)\times \left[\right(7-x)\times {10}^{-6}C]}{(0.3m{)}^2}$

$x^2-7x+10=0$
$x=2\mu C$ or $5\mu C$

Option $B$ is correct.