(15)
its direction being along the axis OX. For a point in the line OY bisecting the magnet perpendicularly, θ = π/2 therefore cos θ = 0, and the point D is at an infinite distance. The magnitude of the force is in this case
Fy = M / r³,
(16)
and its direction is parallel to the axis of the magnet. Although the above useful formulae, (10) to (15), are true only for an infinitely small magnet, they may be practically applied whenever the distance r is considerable compared with the length of the magnet.
| Fig. 4. |
Couples and Forces between Magnets.—If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is
MH sin θ,
(17)
where θ is the angle between the axis of the magnet and the direction of the force. In fig. 4 S′N′ is a small magnet of moment M′, and SN a distant fixed magnet of moment M; the axes of SN and S′N′ make angles of θ and φ respectively with the line through their middle points. It can be deduced from (17), (12) and (13) that the couple on S′N′ due to SN, and tending to increase φ, is