Magnetic Fields & Their Sources

You’ll be able to

Identify moving charges and currents as the source of all magnetic fields
Describe the geometry of magnetic field lines and use the right-hand rule for a wire
Relate the field near a long straight wire to the current and distance

What makes a magnetic field

Every magnetic field traces back to one thing: moving electric charge. An electric current in a wire creates a magnetic field around it, and even the magnetism of a bar magnet comes from the motion and intrinsic spin of its electrons. Stationary charges make only electric fields; you must have charge in motion to get magnetism. Field lines form closed loops — they never begin or end, because there are no magnetic monopoles: you cannot isolate a north pole without its south. Break a magnet in half and each piece is a complete magnet again.

The right-hand rule for a wire

The magnetic field circles a current-carrying wire. To find its direction, use the right-hand rule: point your right thumb along the (conventional) current, and your curled fingers show the way the field wraps around the wire. The field is strongest close to the wire and weakens with distance. Field lines outside a bar magnet run from the north pole to the south pole, then continue through the magnet back to north — always forming complete loops.

Field of a long straight wire

B = μ₀ · I / (2π · r)

μ₀ = 4π × 10⁻⁷ T·m·A⁻¹ is the permeability of free space. B is measured in teslas (T). The field is proportional to the current and inversely proportional to the distance r from the wire.

Worked example

A long straight wire carries a current of 10 A. What is the magnitude of the magnetic field 0.020 m from the wire?

1.Use B = μ₀I / (2πr) with μ₀ = 4π × 10⁻⁷ T·m·A⁻¹.
2.The 4π on top and 2π on the bottom simplify: B = (2 × 10⁻⁷) · I / r.
3.Substitute: B = (2 × 10⁻⁷)(10) / (0.020).
4.Compute: (2 × 10⁻⁶) / 0.020 = 1.0 × 10⁻⁴ T.

Answer: ≈ 1.0 × 10⁻⁴ T (0.1 mT), circling the wire in the direction given by the right-hand rule.

Tip

The combination μ₀/(2π) equals exactly 2 × 10⁻⁷ T·m·A⁻¹. Recognizing that shortcut turns the straight-wire formula into a quick B = (2 × 10⁻⁷)·I/r calculation.

Checkpoint

The magnetic field a distance r from a long straight current-carrying wire has magnitude B. At twice the distance from the same wire, the field is:

Checkpoint

Which of the following is the fundamental source of all magnetic fields?

On the exam

Two facts anchor this topic: magnetism comes from moving charge, and magnetic field lines are always closed loops (no monopoles). If a diagram shows field lines starting or stopping in mid-space, something is wrong.

Answer the 2 checkpoints as you read.