The force of attraction between the charge located at \(x = 3.00{\rm{ cm}}\) and \(x = 8.00{\rm{ cm}}\) is,
\[{F_{11}} = \frac{{K\left( q \right)\left( {2q} \right)}}{{{{\left( {{r_3} - {r_8}} \right)}^2}}}\]
Substitute \(9 \times {10^9}{\rm{ N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}\) for K, \(1.00{\rm{ }}\mu C\) for \(q\), \(3.00{\rm{ cm}}\) for \[{r_3}\] and \(8.00{\rm{ cm}}\) for \[{r_8}\],
\(\begin{array}{c}{{\rm{F}}_{\rm{3}}}{\rm{ = }}\frac{{\left( {9 \times {{10}^9}{\rm{ N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}} \right){\rm{ \times }}\left( {{\rm{1}}{\rm{.00 \mu C}}} \right){\rm{ \times }}\left( {{\rm{2 \times 1}}{\rm{.00 \mu C}}} \right)}}{{{{\left[ {\left( {{\rm{3}}{\rm{.00 cm}}} \right){\rm{ - }}\left( {{\rm{8}}{\rm{.00 cm}}} \right)} \right]}^{\rm{2}}}}}\\{\rm{ = }}\frac{{\left( {9 \times {{10}^9}{\rm{ N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}} \right){\rm{ \times }}\left( {{\rm{1}}{\rm{.00 \mu C}}} \right){\rm{ \times }}\left( {{\rm{2 \times 1}}{\rm{.00 \mu C}}} \right)}}{{{{\left[ {{\rm{ - }}\left( {{\rm{5}}{\rm{.00 cm}}} \right)} \right]}^{\rm{2}}}}}\\{\rm{ = }}\frac{{\left( {9 \times {{10}^9}{\rm{ N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}} \right){\rm{ \times }}\left( {{\rm{1}}{\rm{.00 \mu C}}} \right){\rm{ \times }}\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}}{\rm{ C}}}}{{{\rm{1 \mu C}}}}} \right){\rm{ \times }}\left( {{\rm{2 \times 1}}{\rm{.00 \mu C}}} \right){\rm{ \times }}\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 6}}}}{\rm{ C}}}}{{{\rm{1 \mu C}}}}} \right)}}{{{{\left[ {{\rm{ - }}\left( {{\rm{5}}{\rm{.00 cm}}} \right){\rm{ \times }}\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 2}}}}{\rm{ m}}}}{{{\rm{1 cm}}}}} \right)} \right]}^{\rm{2}}}}}\\{\rm{ = 7}}{\rm{.2 N}}\end{array}\)
The force of attraction between the charge located at \(x = 8.00{\rm{ cm}}\) and \(x = 11.00{\rm{ cm}}\) is,
\[{F_{11}} = \frac{{K\left( {2q} \right)\left( q \right)}}{{{{\left( {{r_8} - {r_{11}}} \right)}^2}}}\]
Substitute \(9 \times {10^9}{\rm{ N}} \cdot {{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{C}}^{\rm{2}}}\) for \(K\), \(1.00{\rm{ }}\mu C\) for \(q\), and \(8.00{\rm{ cm}}\) for \[{r_8}\], and \(11.00{\rm{ cm}}\) for \[{r_{11}}\]
\(\begin{array}{c}{F_{11}} = \frac{{\left( {9 \times {{10}^9}{\rm{ }}N \cdot {m^2}/{C^2}} \right) \times \left( {2 \times 1.00{\rm{ }}\mu C} \right) \times \left( {1.00{\rm{ }}\mu C} \right)}}{{{{\left[ {\left( {8.00{\rm{ }}cm} \right) - \left( {11.00{\rm{ }}cm} \right)} \right]}^2}}}\\ = \frac{{\left( {9 \times {{10}^9}{\rm{ }}N \cdot {m^2}/{C^2}} \right) \times \left( {2 \times 1.00{\rm{ }}\mu C} \right) \times \left( {1.00{\rm{ }}\mu C} \right)}}{{{{\left[ { - \left( {3.00{\rm{ }}cm} \right)} \right]}^2}}}\\ = \frac{{\left( {9 \times {{10}^9}{\rm{ }}N \cdot {m^2}/{C^2}} \right) \times \left( {2 \times 1.00{\rm{ }}\mu C} \right) \times \left( {\frac{{{{10}^{ - 6}}{\rm{ }}C}}{{1{\rm{ }}\mu C}}} \right) \times \left( {1.00{\rm{ }}\mu C} \right) \times \left( {\frac{{{{10}^{ - 6}}{\rm{ }}C}}{{1{\rm{ }}\mu C}}} \right)}}{{{{\left[ { - \left( {3.00{\rm{ }}cm} \right) \times \left( {\frac{{{{10}^{ - 2}}{\rm{ }}m}}{{1{\rm{ }}cm}}} \right)} \right]}^2}}}\\ = 20{\rm{ }}N\end{array}\)
The net force acting on the charge located at \(x = 8.00{\rm{ cm}}\) is,
\(F = \left| {{F_3} - {F_{11}}} \right|\)
Substitute \({\rm{7}}{\rm{.2 }}N\) for \({{\rm{F}}_{\rm{3}}}\) and \(20{\rm{ }}N\) for \({F_{11}}\),
\(\begin{array}{c}F = \left| {\left( {7.2{\rm{ N}}} \right) - \left( {20{\rm{ N}}} \right)} \right|\\ = 12.8{\rm{ N}}\end{array}\)
Hence, force on the charge located at \(x = 8.00{\rm{ cm}}\) is \({\rm{12}}{\rm{.8 }}N\).
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