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  • equal charges q are placed at the four corners of the square length a the maginutude of the forcde on the charge at the corner b will be

equal charges q are placed at the four corners of the square length a the maginutude of the forcde on the charge at the corner b will be

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\begin{aligned} &\text { force on } B \text { due to } A=f_{1}=\frac{k Q^{2}}{a^{2}}\\ &\text { force on } C \text { due to } B=f_{2}=\frac{k Q^{2}}{a^{2}}\\ &\text {resul tan tof these two forces }=f=\sqrt{f_{1}^{2}+f_{2}^{2}}=\sqrt{2} \frac{k Q^{2}}{a^{2}}\\ &\text { force due to } D=f_{3}=\frac{k Q^{2}}{2 a^{2}}\\ \end{aligned}

\begin{aligned} &R=\text { net force }=\sqrt{f^{2}+f_{3}^{2}+2 f_{3} \cos 0}\\ &=f+f_{3}\\ &=\sqrt{2} \frac{k Q^{2}}{a^{2}}+\frac{k Q^{2}}{2 a^{2}}\\ &=\frac{k Q^{2}}{a^{2}}\left(\frac{2 \sqrt{2}+1}{2}\right) \end{aligned}

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