Three point charges $q$, $-2q$ and $2q$ are placed on $x$ axis at a distance $x=0$, $x=\dfrac34R$ and $x=R$ respectively from origin as shown. If $q=2\times10^{-6}\ \text{C}$ and $R=2\ \text{cm}$, the magnitude of net force experienced by the charge $-2q$ is ______ N.
Numerical value type. Enter your answer.
Answer: 5440
With $R=2\ \text{cm}$: $-2q$ is $1.5\ \text{cm}$ from $q$ and $0.5\ \text{cm}$ from $2q$. Both forces on $-2q$ are attractive, towards $q$ (left) and towards $2q$ (right):
$$F_{right}=\frac{k(2q)(2q)}{(0.005)^2},\qquad F_{left}=\frac{k(q)(2q)}{(0.015)^2}$$
$$F=kq^2\left(\frac{4}{2.5\times10^{-5}}-\frac{2}{2.25\times10^{-4}}\right)=9\times10^9\times4\times10^{-12}\times(160000-8889)\approx5440\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics