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.

Sol. Electric force feeled by 1 c due to 1 × 10^–8 c. F base 1 = k * 1 * 10^-8 * 1/(10 * 10^-2)^2 = k * 10^-6 N. electric force feeled by 1 c due to 8 * 10^-8 c. F base 2 = k * 8 *10^-8 * 1/(23 * 10^-2)^2 = k * 8 * * 10^-8 * 10^2/9 = 28k * 10^-6/4 = 2k * 10^-6 N. Similarly F base 3 = k * 27 * 10^-8 * 1/(30 * 10^-2)^2 = 3k * 10^-6 N So, F = F base 1 + F base 2 + F base 3 + ….+ F base 10 = k * 10^-6 (1 + 2 + 3 +…..+ 10) N = k * 10^-6 * 10 * 11/2 = 55k * 10^-6 = 55 * 9 * 10^9 * 10^-6 N = 4.95 * 10^3 N