The Bar Magnet

The figure shows a single, static illustration of iron filings sprinkled on a glass sheet placed over a short bar magnet. The magnet is oriented vertically beneath the sheet. The filings have self-organised into a pattern of curved arcs. Two dense, radiating clusters of filings appear — one near the top end of the magnet and one near the bottom end — fanning outward like a starburst. Between these two clusters, the filings form smooth, curved arcs that bulge outward to the left and right. No labels (N/S) are printed on the figure; the two-pole structure is implied by the symmetry of the pattern.

What the pattern teaches: The iron filings trace the magnetic field lines of the bar magnet. The two dense clusters correspond to the poles of the magnet — the regions where the field is strongest and lines converge or diverge. The smooth arcs between the poles show that the field lines emerge from one pole, curve through space, and re-enter the other pole. This pattern is identical in shape to the electric field lines of an electric dipole (two equal and opposite charges separated by a small distance). Thus, the bar magnet behaves as a magnetic dipole.

Key formula developed from this figure: The magnetic field at a point on the axial line (the line passing through both poles) of a bar magnet of magnetic dipole moment $\vec{m}$ is given by:

where:

• $\vec{B}_{\text{axial}}$ is the magnetic field vector at a point on the axis,
• $\mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1}$ is the permeability of free space,
• $\vec{m}$ is the magnetic dipole moment of the bar magnet (magnitude $m = q_m \cdot 2l$, where $q_m$ is the pole strength and $2l$ is the separation between poles),
• $r$ is the distance from the centre of the magnet to the point (for $r \gg 2l$).

On the equatorial line (the perpendicular bisector of the magnet), the field is: …