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Equal charges $q$ are placed at the four corners $A,\,B,\,C,\,D$ of a square of length $a$. The magnitude of the force on the charge at $B$ will be
$\frac{{3{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
$\frac{{4{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
$\left( {\frac{{1 + 2\sqrt 2 }}{2}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
$\left( {2 + \frac{1}{{\sqrt 2 }}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$
Solution
(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)$
