# 4 equal point charges each 16uC are placed on the 4 corners of a square of side 0.2m . calculate the force on any 1 of the charges?

Mar 17, 2018

Suppose,the $4$ like charges are present at $A , B , C , D$ and $A B = B C = C D = D A = 0.2 m$

We are considering forces on $B$;so due to $A$ and $C$ force($F$) will be repulsive in nature along $A B$ and $C B$ respectively.

due to $D$ force ($F '$) will also be repulsive in nature acting along diagonal $D B$

$D B = 0.2 \sqrt{2} m$

So,$F = \frac{9 \cdot {10}^{9} \cdot {\left(16 \cdot {10}^{-} 6\right)}^{2}}{0.2} ^ 2 = 57.6 N$

and $F ' = \frac{9 \cdot {10}^{9} \cdot {\left(16 \cdot {10}^{-} 6\right)}^{2}}{0.2 \sqrt{2}} ^ 2 = 28.8 N$

now,$F '$ makes an angle of ${45}^{\circ}$ with both $A B$ and $C B$.

so,component of $F '$ along two perpendicular direction i.e $A B$ and $C B$ will be $28.8 \cos 45$

So,we have two forces of $\left(57.6 + 28.8 \cos 45\right) = 77.95 N$ acting perpendicular to each other on the charge at $B$

So,net force on the charge at $B$ is $\sqrt{{77.95}^{2} + {77.95}^{2}} = 77.95 \sqrt{2} = 110.24 N$ making an angle of ${45}^{\circ}$ w.r.t $A B$ and $C B$