Question

If a magnet is carefully broken into two equal pieces as shown in Fig, how does the magnetic strength of each piece compare with that of the original magnet ?

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is B $1:2$

The surface field strength of a magnet is only a function of its shape, not its size. Long thin magnets with poles at each end have a very intense magnetic field at each pole, more so than a short fat magnet, but only over a small area. They do have good reach though, we still have significant, although not terribly strong field at about one length, much more than a shorter magnet of the same diameter.
The distance that the magnet casts a magnetic field gets smaller as the magnet gets smaller. So the half-size magnet would have a half-sized magnetic field strength at a distance. The ratio of the magnetic strength of smaller magnet to the original size magnet is given as 1:2.
A magnet could cause a measurable decrease in strength; but it would depend on the material. For example, neodymium magnets probably not very much at all, may not be measurable, whereas ferrites it could be quite a lot.