Non vorrei insistere, ho capito i vostri procedimenti ma ancora c'è qualcosa che non mi convince nel mio.. non capisco cosa c'è, in fondo in fondo, di sbagliato. Ho corretto le formule tenendo conto che alcune forze sono attrattive e altre repulsive:
\(\overrightarrow{F}{}^{}_{2}= \frac{q^2}{4\pi \varepsilon } \frac{1} {r^2} \overrightarrow{u}{}_{y}=\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2}
\overrightarrow{u}{}_{y};\)
\(F{}^{}_{2,y}= \frac{q^2}{4\pi \varepsilon} \frac{y{}_{0}-y{}_{2}} {[(x{}_{0}-x{}_{2})^2+(y{}_{0}-y{}_{2})^2+(z{}_{0}-z{}_{2})^2]^{\frac{3}{2}}}=
\frac{q^2}{4\pi \varepsilon} \frac{2a}{[(2a)^2]^{\frac{3}{2}}}= \frac{q^2}{4\pi \varepsilon} \frac{2a}{[4a{}^{2}]^{\frac{3}{2}}}=\frac{q^2}{16 a^2 \pi
\varepsilon};\)
\(\overrightarrow{F}{}^{}_{4}= \frac{-q^2}{4\pi \varepsilon } \frac{1} {r^2} \overrightarrow{u}{}_{z}=\frac{-q^2}{4\pi \varepsilon } \frac{1} {(2a)^2}
\overrightarrow{u}{}_{z}=\frac{-q^2}{4\pi \varepsilon } \frac{1} {4(a)^2} \overrightarrow{u}{}_{z}=\frac{-q^2}{16 a^2 \pi \varepsilon }
\overrightarrow{u}{}_{z};\)
\(F{}^{}_{4,z}= -\frac{q^2}{4\pi \varepsilon} \frac{z{}_{0}-z{}_{4}} {[(x{}_{0}-x{}_{4})^2+(y{}_{0}-y{}_{4})^2+(z{}_{0}- z{}_{4})^2]^{\frac{3}{2}}}=
-\frac{q^2}{4\pi \varepsilon} \frac{2a}{[(2a)^2]^{\frac{3}{2}}}=- \frac{q^2}{4\pi \varepsilon} \frac{2a}{[4a{}^{2}]^{\frac{3}{2}}}=-\frac{q^2}{16 a^2 \pi
\varepsilon};\)
\(\overrightarrow{F}{}^{}_{3}=\overrightarrow{F}{}^{}_{3,y} + \overrightarrow{F}{}^{}_{3,z} =-\frac{q^2}{4\pi \varepsilon} \frac{1} {r^2}
\overrightarrow{u}{}_{y} - \frac{q^2}{4\pi \varepsilon} \frac{1} {r^2} \overrightarrow{u}{}_{z} =
-\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2} \overrightarrow{u}{}_{y}-\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2} \overrightarrow{u}{}_{z};\)
\(F{}^{}_{3,y}= -\frac{q^2}{4\pi \varepsilon} \frac{y{}_{0}-y{}_{3}} {[(x{}_{0}-x{}_{3})^2+(y{}_{0}-y{}_{3})^2+(z{}_{0}-z{}_{3})^2]^{\frac{3}{2}}}=-
\frac{q^2}{4\pi \varepsilon} \frac{2a}{[(2a)^2+(2a)^2]^{\frac{3}{2}}}= -\frac{q^2}{4\pi \varepsilon} \frac{2a}{[8a{}^{2}]^{\frac{3}{2}}}=-\frac{q^2}{4
\pi \varepsilon} \frac{1}{8\surd2a^2 }=-\frac{q^2}{32 \surd2 a^2\pi \varepsilon } ;\)
\(F{}^{}_{3,z}= -\frac{q^2}{4\pi \varepsilon} \frac{z{}_{0}-z{}_{3}} {[(x{}_{0}-x{}_{3})^2+(y{}_{0}-y{}_{3})^2+(z{}_{0}-z{}_{3})^2]^{\frac{3}{2}}}=-
\frac{q^2}{4\pi \varepsilon} \frac{2a}{[(2a)^2+(2a)^2]^{\frac{3}{2}}}= -\frac{q^2}{4\pi \varepsilon} \frac{2a}{[8a{}^{2}]^{\frac{3}{2}}}=-\frac{q^2}{4
\pi \varepsilon} \frac{1}{8\surd2a^2 }=-\frac{q^2}{32 \surd2 a^2\pi \varepsilon } ;\)
\( \overrightarrow{F}{}^{}_{1}= \overrightarrow{F}{}^{}_{0}= \overrightarrow{F}{}^{}_{2} +\overrightarrow{F}{}^{}_{3}+\overrightarrow{F}{}^{}_{4}=
\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2} \overrightarrow{u}{}_{y} -\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2} \overrightarrow{u}{}_{y}-
\frac{q^2}{4\pi \varepsilon } \frac{1} {(2a)^2} \overrightarrow{u}{}_{z} -\frac{q^2}{16 a^2 \pi \varepsilon } \overrightarrow{u}{}_{z}= 0; \)
Perciò chiedo, forse ottusamente, cosa sbaglio ancora? Che mi sfugge?!
Grazie ancora per la pazienza e le eventuali, oltre che precedenti, risposte.