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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.
Solution
By Coulomb's Law, force (F) on charge q due to one charge,
\[F = F_1 + F_2 + F_3 + . . . . . + F_{10} \]
\[ = 9 \times {10}^9 \times \left[ \frac{1 . 0}{\left( 0 . 10 \right)^2} + \frac{8}{\left( . 20 \right)^2} + \frac{27}{\left( . 30 \right)^2} + . . . . . . \frac{1000}{\left( 1 . 0 \right)^2} \right] {10}^{- 8} \]
\[ = \frac{9 \times {10}^9 \times {10}^{- 8}}{{10}^{- 2}}\left[ 1 + 2 + 3 + . . . . . . 10 \right]\]
\[ = 9 \times {10}^3 \times 55\]
\[ = 4 . 95 \times {10}^5\] N
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