Question

Calculate the net force acting on the charge present at the origin.

• A. $\frac{q{q}_1}{4\pi {ϵ}_0{a}^2}\times \sqrt{2}$
• B. $\frac{q{q}_1}{4\pi {ϵ}_0\sqrt{2}{a}^2}+\frac{q{q}_1}{8\pi {ϵ}_0{a}^2}$
• C. $\frac{q{q}_1}{4\pi {\left(ϵ\right)}_0{a}^2}(\sqrt{2}+\frac{1}{2})$
• D. $\frac{q{q}_1}{4\pi {\left(ϵ\right)}_0{a}^2}(\frac{1}{2}-\sqrt{2})$

Answer 1

Answer: (C)

$F_1=k\frac{q{q}_1}{a^2};F_2=k\frac{q{q}_1}{(\sqrt{2}a{)}^2}$
Resultant force $F=\sqrt{2}{F}_1+F_2$
$=\sqrt{2}\frac{kq{q}_1}{a^2}+\frac{kq{q}_1}{2a^2}$
$=\frac{kq{q}_1}{a^2}(\sqrt{2}+\frac{1}{2})$
$=\frac{q{q}_1}{4\pi {\left(ϵ\right)}_0{a}^2}(\sqrt{2}+\frac{1}{2})$