Question

Four charges of +q, -q, +q and +q are placed at the corners A, B, C and D of a square. The resultant force on the charge at D is

• A. $\frac{q^2}{4\pi {ϵ}_0{a}^2}(\sqrt{2}-\frac{1}{2})$
• B. $\frac{2q^2}{\pi {ϵ}_0{a}^2}$
• C. $\frac{q^2}{8\pi {ϵ}_0{a}^2}2\sqrt{2}$
• D. $zero$

Answer 1

The correct option is A $\frac{q^2}{4\pi {ϵ}_0{a}^2}(\sqrt{2}-\frac{1}{2})$

$F_{AC}=\sqrt{2}{F}_A=\sqrt{2}\frac{1}{4\pi {ϵ}_0}\frac{q^2}{a^2}\to \left(1\right)$
$F_B=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{(\sqrt{2}a{)}^2}=\frac{1}{1\pi {ϵ}_0}\frac{q^2}{2a^2}\to \left(2\right)$
$F_R=F_{AC}-F_B=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{a^2}[\sqrt{2}-\frac{1}{2}]$