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 k=0.0064. Find the work required to move the magnets from a distance of 0.03m apart to a distance of 0.09 m apart.

Answer 1

Work = (0.0064/0.09^2) - (0.0064/0.03^2) = 0.0064/0.0081 = 0.79 mJ

Answer 2

AAAaannndd the bot gets it wrong yet again!
since the force is not constant, the simple work=Fd does not work.
Also, (0.0064/0.09^2) - (0.0064/0.03^2) = -6.32

The work is
∫[0.3,0.9] 0.0064/r^2 dr = 0.0142

Answer 3

Huh? That is the difference in forces.
F = k/x^2
work = integral F dx
= k * integral from x = .03 to x = .09 of 1/x^2
= -k ( 1/.09 - 1/.03)
= - k (11.1 - 33.3) = 22.2 k = 22.2 * 0064 = .142 Joules

note integral (dx/x^2) = -1/x