Two charges of 10 nC each are spaced 80 cm from each other. What work must be done to bring them closer to 10 cm?

Let there be given two charges q₁ = q₂ = q = 10 nC = 10 ∙ 10⁻⁹ C, located at a distance of R₁ = 80 cm = 0.8 m from each other. To determine what work must be done against the forces of electrostatic interaction in order to bring the charges closer to a distance of R₂ = 10 cm = 0.1 m, it is required to calculate the potential energy of interaction of charges in the first case W₁ and in the second case W₂. The work will be equal to the change in energy: A = W₂ – W₁.

First, W₁ = k ∙ q² / R₁, where the coefficient k = 9 ∙ 10⁹ N ∙ m² / Kl², after moving W₂ = k ∙ q² / R₂, then work: A = k ∙ q² ∙ (R₁– R₂) / (R₁ ∙ R₂).

Let’s substitute the values ​​of physical quantities in the calculation formula and make calculations: А = k ∙ q² ∙ (R₁– R₂) / (R₁ ∙ R₂); A = 7875 ∙ 10⁻⁹ J. Answer: it is necessary to do the work of 7.875 μJ.