Question

Ten positively-charged particles are kept fixed on the x-axis at points x = 10 cm, 20 cm, 30 cm, ...., 100 cm. the first particle has a charge 1.0 × 10⁻⁸ C, the second 8 × 10⁻⁸ C, the third 27 × 10⁻⁸ C and so on. The tenth particle has a charge 1000 × 10⁻⁸ C.  Find the magnitude of the electric force acting on a 1 C charge placed at the origin. 

Answer 1

By Coulomb's Law, force (F) on charge q due to one charge,            

$$F=\frac{1}{4\pi {ϵ}_0}\frac{q_{1}q}{r^2}$$

So, net force due to ten charges, 

$$F=F_1+F_2+F_3+.....+F_{10}$$ 

$$=9\times {10}^9\times [\frac{1.0}{{(0.10)}^2}+\frac{8}{{(.20)}^2}+\frac{27}{{(.30)}^2}+......\frac{1000}{{(1.0)}^2}]{10}^{-8}$$ 

$$=\frac{9\times {10}^9\times {10}^{-8}}{{10}^{-2}}[1+2+3+......10]$$ 

$$=9\times {10}^3\times 55$$ 

$$=4.95\times {10}^5$$ N