Question

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

• A. $1\mu C$ and $6\mu C$
• B. $2\mu C$ and $-5\mu C$
• C. $3\mu C$ and $4\mu C$
• D. $2\mu C$ and $5\mu C$

Answer 1

The correct option is D $2\mu C$ and $5\mu C$

$q_1+q_2=7\mu C$

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

$⟹\frac{9\times {10}^9\times q_1{q}_2}{(0.3{)}^2}=1N$

$⟹q_1{q}_2={10}^{-11}=10(\mu C{)}^2$

Now, $q_1-q_2=\sqrt{(q_1+q_2{)}^2-4q_1{q}_2}$

$⟹q_1-q_2=3\mu C$

And, $q_1+q_2=7\mu C$

Hence, $q_1=5\mu C$ and $q_2=2\mu C$

Answer-(D)