What Produces a Magnetic Field? — Question 5

Question 5

Cutting a uniformly magnetized bar produces smaller dipoles rather than isolated poles

A uniformly magnetized bar points from its south end toward its north end. It is cut perpendicular to that direction into three equal pieces without changing their magnetization. Its original magnetic moment is $\vec\mu_0$; moment is proportional to magnetized volume in this model.

1. Identify the poles on each piece and count exposed north and south pole faces.

2. Find the moment of each piece and their vector sum before any piece is rotated.

Question 5 - Solution

Cutting a uniformly magnetized bar produces smaller dipoles rather than isolated poles

(a) Method and calculation

$$\text{Each piece: S}\longrightarrow\text{N}.$$$$N_{\mathrm{north}}=3,\quad N_{\mathrm{south}}=3,\quad N_{\mathrm{north}}-N_{\mathrm{south}}=0.$$

(b) Interpretation and further calculation

$$\vec\mu_i=\vec\mu_0/3\quad(i=1,2,3).$$$$\sum_{i=1}^3\vec\mu_i=\vec\mu_0.$$New opposite pole faces appear at each cut; none of the pieces is a magnetic monopole.

Physical check

The equal-moment result assumes preserved uniform magnetization; cutting can change magnetization in real materials.