Module 2 : Electrostatics
Lecture 8 : Coulomb's Law
Example 1:
 

Two positive charges 2 nC each are placed along the x-axis at $\pm 3$m. A third charge of opposite sign with magnitude 3 nC is placed on the y-axis at $(0,4)$m. Find the net force on the charge on the y-axis due to the other two charges.
Solution :
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The forces are attractive and are shown. The magnitude of each force is
\begin{displaymath}F_1 = F_2 = \frac{1}{4\pi\epsilon_0}\frac {3\times 10^{-9}\cdot 2 \times 10^{-9}}{5^2} = (54/25)\times 10^{-9}\;\; {\rm N}\end{displaymath}
The angle $\theta$is $\sin^{-1}(3/5)$. Clearly, $ F_{1x}=-F_{2x}$and the x-components cancel. The net force is towards the origin along the y-axis and is
\begin{displaymath}F_{net} = F_{1y} + F_{2y} = (F_1 + F_2)\cos\theta = 3.46\times 10^{-9} \;\;{\rm N}\end{displaymath}
 
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