Three point charges of magnitude $5\ \mu\text{C}$, $0.16\ \mu\text{C}$ and $0.3\ \mu\text{C}$ are located at the vertices $A$, $B$, $C$ of a right angled triangle whose sides are $AB = 3\ \text{cm}$, $BC = 3\sqrt2\ \text{cm}$ and $CA = 3\ \text{cm}$, and point $A$ is the right angle corner. The charge at point $A$ experiences ______ N of electrostatic force due to the other two charges.
Numerical value type. Enter your answer.
Answer: 17
$$F_{AB} = \frac{9\times10^9\times5\times10^{-6}\times0.16\times10^{-6}}{(0.03)^2} = 8\ \text{N},\qquad F_{AC} = \frac{9\times10^9\times5\times10^{-6}\times0.3\times10^{-6}}{(0.03)^2} = 15\ \text{N}$$
The two forces are perpendicular (right angle at $A$):
$$F = \sqrt{8^2 + 15^2} = 17\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics