Calculus Helppppp

Question

The strength of magnetic force varies inversely with the square of the distance between the magnets. In other words, force = k/distance^2 Suppose that when two magnets are 4 cm apart, there is a force of 2 newtons. Find the work required to move the magnets from a distance of 2 cm apart to a distance of 11 cm apart.

In your work, please show the set-up integral you used to find the work.

Answer 1

F= k/d²; k = Fd² = 2N·(0.04)²m² = 0,0032 Jm

Elementary work dA = F(x)dx = kdx/x²; A = ∫_0.02^0.11kdx/x² = - k/x_0.02^0.11 = 0.0032(1/0.02 - 1/0.11) = 0.131 J