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The net force on particle A is$2.014脳{10}^{鈭�23}\mathrm{N}$in the negative direction of the x-axis.

The net force on A is$2.877脳{10}^{鈭�23}N$in the negative direction of the x-axis.

Using the same concept of Coulomb's law, we can get the proportionality relation of charge and force. Hence, this is used to find the required ratio of the charges.

Formula:

The magnitude of the electrostatic force between any two particles,

$\mathrm{F}=\mathrm{k}\frac{\left|{\mathrm{q}}_1\right|\left|{\mathrm{q}}_2\right|}{{\mathrm{r}}^2}$ (1)

Since the forces involved are proportional to q, we see that the essential difference between the two situations is ${\mathrm{F}}_{\mathrm{a}}鈭�{\mathrm{q}}_{\mathrm{B}}+{\mathrm{q}}_{\mathrm{C}}$ (when those two charges are on the same side) versus ${\mathrm{F}}_{\mathrm{b}}鈭�鈭�{\mathrm{q}}_{\mathrm{B}}+{\mathrm{q}}_{\mathrm{C}}$ (when they are on opposite sides). Setting up ratios considering the equation (1), we have the given relation:

$\begin{array}{c}\frac{{\mathrm{F}}_{\mathrm{a}}}{{\mathrm{F}}_{\mathrm{b}}}=\frac{{\mathrm{q}}_{\mathrm{B}}+{\mathrm{q}}_{\mathrm{C}}}{鈭�{\mathrm{q}}_{\mathrm{B}}+{\mathrm{q}}_{\mathrm{C}}}\\ \frac{2.014脳{10}^{鈭�23}\mathrm{N}}{鈭�2.877脳{10}^{鈭�23}\mathrm{N}}=\frac{1+{\mathrm{q}}_{\mathrm{C}}/{\mathrm{q}}_{\mathrm{B}}}{鈭�1+{\mathrm{q}}_{\mathrm{C}}/{\mathrm{q}}_{\mathrm{B}}}\\ 鈭�7=\frac{1+{\mathrm{q}}_{\mathrm{C}}/{\mathrm{q}}_{\mathrm{B}}}{鈭�1+{\mathrm{q}}_{\mathrm{C}}/{\mathrm{q}}_{\mathrm{B}}}\end{array}$

Therefore,

$\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{C}}}{{\mathrm{q}}_{\mathrm{B}}}=\frac{7+1}{7鈭�1}\\ =1.33\end{array}$

Hence, the value of the required ratio is $1.33$