Find the work done?

Question

According to Coulombs Law, two like electrical charges repel each other with a force that is inversely proportional to the square of the distance between them. If the force of repulsion is 10 dynes (1 dyne = 10E-5 newton) when they are 2 cm apart, find the work done in bringing the charges from 5 cm apart to 1 cm apart.

Answer 1

The force between two charges: F = e1*e2/(4*pi*epsilon*r^2)
What is given: 10 dynes = e1*e2/(4*pi*epsilon*(2cm)^2)
The work done: [Integral from 5cm to 1cm] F(r)dr
= e1*e2/(4*pi*epsilon*(r)) (evaluated from 1cm to 5cm)
= e1*e2/(4*pi*epsilon)*(1/(1cm) - 1/(5cm))
= (10dynes)*(2cm)*(2/1 -2/5)
= 32 erg