Đáp án:
$\begin{array}{l} q_1=4.10^{-7}C \\ q_2=2.10^{-7}C \end{array}$
Giải:
Khi chưa tiếp xúc:
`F=k\frac{q_1q_2}{r^2}`
⇔ `0,288=9.10^9.\frac{q_1q_2}{0,05^2}`
⇒ `q_1q_2=8.10^{-14}` (1)
Khi đã tiếp xúc:
$q'_1=q'_2=\dfrac{q_1+q_2}{2}$
→ $q'_1q'_2=(\dfrac{q_1+q_2}{2})^2=\dfrac{(q_1+q_2)^2}{4}$
$F'=k\dfrac{q'_1q'_2}{r^2}=k\dfrac{(q_1+q_2)^2}{4r^2}$
⇔ `0,324=9.10^9.\frac{(q_1+q_2)^2}{4.0,05^2}`
⇔ `(q_1+q_2)^2=3,6.10^{-13}`
⇒ `q_1+q_2=6.10^{-7}` (2)
Thay (2) vào (1)
→ `q_1(6.10^{-7}-q_1)=8.10^{-14}`
⇔ `q_1^2-6.10^{-7}q_1+8.10^{-14}=0`
⇒ `q_1=4.10^{-7} \ (C)`
⇒ `q_2=2.10^{-7} \ (C)`
