The Bar Magnet

When iron filings are sprinkled on a glass sheet placed over a bar magnet, they arrange themselves in curved lines running from one end of the magnet to the other. This pattern matches the electric field pattern around an electric dipole, which is why a bar magnet is called a magnetic dipole. The same pattern also appears around a current-carrying solenoid, hinting that magnets and electric currents produce the same type of field.

Picture a rectangular bar magnet lying horizontally:

• XX′ is the axis — an imaginary line running through both poles.
• YY′ is the equator — the perpendicular line through the magnet's centre.
• +q_m is the pole strength of the North pole; −q_m is the pole strength of the South pole (unit: A·m).
• D is the geometric length — the physical length you'd measure with a ruler.
• 2l is the magnetic length — the effective distance between the two poles used in calculations.

Key Fact: For every bar magnet, the magnetic length is about 84% of the geometric length: 2l / D = 0.84. Use this ratio unless a problem specifies otherwise.

The magnetic dipole moment (m) measures how strongly a magnet can align with, or influence, a magnetic field. It always points from the South pole to the North pole, inside the magnet.

• SI Unit: Ampere-square metre (A·m²)
• Direction: South pole → North pole (inside the magnet)

• Every bar magnet has two poles; breaking it never isolates a single pole — each piece becomes a smaller complete magnet.
• Magnetic force is strongest at the poles and weakest at the centre.
• A freely suspended magnet aligns its North pole toward Earth's magnetic north and its South pole toward Earth's magnetic south.
• Like poles repel; unlike poles attract.
• Bar magnets attract ferromagnetic materials (iron, steel, nickel, cobalt) that enter their field.

Common Misconception: Students often think cutting a magnet could produce an isolated N or S pole. In reality, magnetic monopoles do not exist — every fragment is a complete dipole.

A bar magnet with pole strength q_m​, dipole length 2l, and magnetic moment m is cut along its length into two equal parts. Find the new pole strength and magnetic moment of each piece.

Solution: Cutting along the length halves the pole strength while the length stays the same.

Each half retains the original magnetic length but only half the pole strength, so its magnetic moment is exactly half the original.

Think of a compass needle — it is simply a tiny bar magnet. When freely suspended, its North pole swings to point toward the Earth's geographic north, and its South pole points south, just like a full-size bar magnet would.