Answer to Question #125416 in Electricity and Magnetism for Anas a

Question

Magnet A has thrice the magnetic field strength of magnet B and at a certain distance pulls on magnet B with a force of 100 Newtons. With how much force, then, does magnet B pull on magnet A? What is the force if the distance between the magnets is doubled?

Answer 1

(a) Magnets A and B are pulling equally on each other (Newton's Third Law). if A pulls on B with 100 N, then B also pulls on A with 100 N.

(b) The force of interaction between the magnets is inversely proportional to the fourth power of the distance between them, which is a consequence of the dipole-dipole nature of the interaction (for non-existent point magnetic charges, this force would, as usual, be inversely proportional to the square of the distance).

So,

$100=\frac{k}{r^4}$ and $f=\frac{k}{(2r)^4}$ $\to$ $100\cdot r^4=f\cdot 2^4\cdot r^4 \to f=\frac{100}{2^4}=6.25 N$