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Three charges $-{{q}_{1}},+{{q}_{2}}$ and $-{{q}_{3}}$ are place as shown in the figure. The $x$ - component of the force on $-{{q}_{1}}$ is proportional to
(b) Force on charge ${{q}_{1}}$ due to ${{q}_{2}}$ is ${{F}_{12}}=k\frac{{{q}_{1}}{{q}_{2}}}{{{b}^{2}}}$
Force on charge ${{q}_{1}}$ due to ${{q}_{3}}$ is ${{F}_{13}}=k\frac{{{q}_{1}}{{q}_{3}}}{{{a}^{2}}}$
The $X$ - component of the force $\left( {{F}_{x}} \right)$ on ${{q}_{1}}$ is ${{F}_{12}}+{{F}_{13}}sin\theta $
$\therefore {{F}_{x}}=k\frac{{{q}_{1}}{{q}_{2}}}{{{b}^{2}}}+k\frac{{{q}_{1}}{{q}_{2}}}{{{a}^{2}}}sin\theta $
$\therefore {{F}_{x}}\propto \frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}sin\theta $
