When sugar is poured from the box into the sugar bowl, the rubbing of sugar grains creates a static electric charge that repels the grains, and causes sugar to go flying out in all directions. If each of two sugar grains acquires a charge of 1.79 x 10-11 C at a separation of 3.45 x 10-5 m, with what force will they repel each other?

2.6*10⁻³ N

Explanation:

From coulomb's law,

F = kq'q/r² ... Equation 1

Where F = Repulsive force, q' = charge on the first sugar grain, q = charge on the second sugar grain, r = distance of separation between the sugar grain, k = proportionality constant.

From the question,

since q' = q

Then,

F = kq²/r² ... Equation 2

Given: q = 1.79*10⁻¹¹ C, r = 3.45*10⁻⁵ m,

Constant: k = 9*10⁹ Nm²/kg².

Substitute into equation 2

F = 9*10⁹ (1.79*10⁻¹¹) ² / (3.45*10⁻⁵) ²

F = 9*10⁹ (3.2041*10⁻²²) / (11.9025*10⁻¹⁰)

F = (28.8369*10⁻¹³) / (11.9025*10⁻¹⁰)

F = 2.6*10⁻³ N.