Question

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

• A. $\frac{3q^2}{4\pi {ϵ}_0{a}^2}$
  
• B. $\frac{4q^2}{4\pi {ϵ}_0{a}^2}$
  
• C. $\left(\frac{1+2\sqrt{2}}{2}\right)\frac{q^2}{4\pi {ϵ}_0{a}^2}$
  
• D. $(2+\frac{1}{\sqrt{2}})\frac{q^2}{4\pi {ϵ}_0{a}^2}$

Answer 1

The correct option is C $\left(\frac{1+2\sqrt{2}}{2}\right)\frac{q^2}{4\pi {ϵ}_0{a}^2}$


After following the guidelines mentioned above

$F_{net}=F_{AC}+F_D=\sqrt{F_A^2+F_C^2}+F_{D}Since{F}_A=F_C=\frac{k{q}^2}{a^2}and{F}_D=\frac{k{q}^2}{(a\sqrt{2}{)}^2}{F}_{net}=\frac{\sqrt{2}k{q}^2}{a^2}+\frac{k{q}^2}{2a^2}=\frac{k{q}^2}{a^2}(\sqrt{2}+\frac{1}{2})=\frac{q^2}{4\pi {ϵ}_0{a}^2}\left(\frac{1+2\sqrt{2}}{2}\right)$