Question

Two point charges $q_1$ and $q_2$ are $3m$ apart and their combined charge is $20\mu C$. If one repels the other with a force of $0.075N$, what are two charges?

• A. $10\mu C,10\mu C$
• B. $19\mu C,1\mu C$
• C. $15\mu C,5\mu C$
• D. $16\mu C,4\mu C$

Answer 1

The correct option is C $15\mu C,5\mu C$

$q_1+q_2=20\mu C$

$⟹q_1=20-q_2$

$F=\frac{q_1{q}_2}{4\pi {ϵ}_o{R}^2}$

$⟹0.075=9\times {10}^9\times \frac{q_1{q}_2}{3^2}$

$⟹q_1{q}_2=0.075\times {10}^{-9}=75\times {10}^{-12}{C}^2$

$⟹q_1{q}_2=75\mu C^2$

$⟹q_2(20-q_2)=75$

$⟹q_2^2-20q_2+75=0$

$⟹(q_2-15)(q_2-5)=0$

$⟹q_2=15\mu C$

$q_1=20-q_2=5\mu C$

Answer-(C)