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,            

\[F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q}{r^2}\]

So, net force due to ten charges, 

\[F =  F_1  +  F_2  +  F_3  +  .  .  .  .  .  +  F_{10} \] 

\[       = 9 \times  {10}^9  \times \left[ \frac{1 . 0}{\left( 0 . 10 \right)^2} + \frac{8}{\left( . 20 \right)^2} + \frac{27}{\left( . 30 \right)^2} + . . . . . . \frac{1000}{\left( 1 . 0 \right)^2} \right] {10}^{- 8} \] 

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

\[         = 9 \times  {10}^3  \times 55\] 

\[         = 4 . 95 \times  {10}^5\] N