c
(c) After following the guidelines mentioned above
\({F_{net}} = {F_{AC}} + {F_D} = \sqrt {F_A^2 + F_C^2 + } {F_D}\)
Since \({F_A} = {F_C} = \frac{{k{q^2}}}{{{a^2}}}\)and \({F_D} = \frac{{k{q^2}}}{{{{(a\sqrt 2 )}^2}}}\)
\({F_{net}} = \frac{{\sqrt 2 k{q^2}}}{{{a^2}}} + \frac{{k{q^2}}}{{2{a^2}}} = \frac{{k{q^2}}}{{{a^2}}}\left( {\sqrt 2 + \frac{1}{2}} \right)\)\( = \frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}\left( {\frac{{1 + 2\sqrt 2 }}{2}} \right)\)