The strength of magnetic force varies inversely with the square of the distance between the magnets. In other words,

$\displaystyle \text{Force}=\frac{{k}}{\text{distance}^{{2}}}$

Suppose that when two magnets are 5 cm apart, there is a force of 3 newtons. Find the work required to move the magnets from a distance of 3 cm apart to a distance of 8 cm apart.
State your answer in Joules. This problem requires calculus.

Work = Preview Question 6   Joules

Note: $\displaystyle {1}\ \text{ Joule}={1}\ \text{ Newton}\cdot\text{meter}$