Question

Two point charges are $3m$ apart and their combined charge is $8\mu C$. The force of repulsion between them is $0.012N$. Charges are

• A. $4\mu C,4\mu C$
• B. $6\mu C,2\mu C$
• C. $5\mu C,3\mu C$
• D. $7\mu C,1\mu C$

Answer 1

Answer: (B)

$q_1+q_2=8\mu C$ ....(i)
$F=0.012N$
or, $k\frac{q_1{q}_2}{r^2}=0.012$
or, $9\times 10^9\times \frac{q_1{q}_2}{3^2}=0.012$
or, $q_1{q}_2=12\times 10^{-12}C$ ...(ii)_
Now, $(q_1-q_2{)}^2=(q_1+q_2{)}^2-4q_1{q}_2$
$=8^2-4\times 12$ [Using eqn (i) arid (iii)]
$=16$
$q_1-q_2=\pm 4\mu C$ ...(iii)
Solving eqn (i) and (iii), we get, charges are $6\mu C$ and $2\mu C$