Đáp án:
\(\begin{array}{l}
TH1:\\
\left\{ \begin{array}{l}
{r_1} = 1,8cm\\
{r_2} = 7,2cm
\end{array} \right.\\
TH2:\\
\left\{ \begin{array}{l}
{r_1} = 3cm\\
{r_2} = 12cm
\end{array} \right.
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{*{20}{l}}
{{E_1} = 4{E_2}}\\
{{\rm{\;}} \Rightarrow k\dfrac{{|{q_1}|}}{{r_1^2}} = 4k\dfrac{{|{q_2}|}}{{r_2^2}}}\\
{ \Rightarrow |\dfrac{{{q_1}}}{{{q_2}}}| = 4\frac{{r_1^2}}{{r_2^2}}}\\
{{\rm{\;}} \Rightarrow |\dfrac{{{{2.10}^{ - 6}}}}{{ - {{8.10}^{ - 6}}}}| = 4{{\dfrac{{{r_1}}}{{{r_2}}}}^2}}\\
{{\rm{\;}} \Rightarrow 0,25 = \dfrac{{{r_1}}}{{{r_2}}}}\\
{ \Rightarrow {r_1} = 0,25{r_2}}
\end{array}\)
TH1: M nằm giữa AB:
\(\begin{array}{l}
{r_1} + {r_2} = 9\\
\Rightarrow \left\{ \begin{array}{l}
{r_1} = 1,8cm\\
{r_2} = 7,2cm
\end{array} \right.
\end{array}\)
TH2: M nằm ngoài AB:
\(\begin{array}{l}
{r_2} - {r_1} = 9\\
\Rightarrow \left\{ \begin{array}{l}
{r_1} = 3cm\\
{r_2} = 12cm
\end{array} \right.
\end{array}\)
