Magnetism and Matter

Lesson

Part 1 — the bar magnet as a magnetic dipole: its field lines, its field at a point, the torque on it, and magnetic flux.

In this lesson you will

Compare a bar magnet with its equivalent solenoid, and magnetic field lines with electric field lines
Use the end-on and broadside-on formulae for the field of a magnet, and find the torque on a magnet in a uniform field
Calculate magnetic flux and convert between tesla, weber per square metre and gauss

Diagram

The bar magnet and its field lines

Field lines of a bar magnet, traced with a small compass or iron filings:

Outside the magnet they run from the N pole round to the S pole; inside they continue from S to N.
Every line is a closed loop; lines never cross.
The magnetic moment $\vec m$ points from S to N inside the magnet (unit A m²).
Breaking a magnet gives two complete magnets: no isolated pole (monopole) has ever been found.

Diagram

A bar magnet as an equivalent solenoid

A short solenoid carrying a current has the same field pattern as a bar magnet: the end where the current is anticlockwise as seen from outside acts as N. Its moment is $m = NIA$

In a magnet, the electrons of each atom act as tiny current loops; in a magnet they are aligned, so their effects add like the turns of a solenoid.
Inside currents of neighbouring loops cancel, leaving a net current round the surface: an equivalent solenoid.

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