Magnetism & Magnetic Fields

Chapter 3 named Ørsted's 1820 discovery twice as the trigger for everything that followed. This chapter gives it the full treatment — and, in the process, corrects a popular version of the story this course itself repeated one chapter ago.

Magnetism Before Electricity

Magnetism was studied for centuries before anyone suspected any connection to electricity. Lodestones (naturally magnetised rock) and magnetic compasses were already in real, practical use for navigation well before the science behind them was understood. William Gilbert's 1600 book De Magnete gave the first real, rigorous account of why a compass points north — correctly proposing that the Earth itself is a giant magnet, tested with a spherical lodestone model he called a "terrella." Before Gilbert's own real, tested explanation, some believed a compass was drawn instead to the pole star Polaris, or to a large magnetic island somewhere at the North Pole — genuine period beliefs Gilbert's own real experimental work displaced.

Ørsted's Real 1820 Discovery

Chapter 3 described Ørsted's discovery, in passing, the way it's very commonly told: an accidental observation during a lecture demonstration, a compass needle happening to twitch near a live wire. That popular version is genuinely a myth.

The Magnetic Field Around a Wire

A long, straight, current-carrying wire produces a magnetic field circling around it:

Here I is the current, r is the perpendicular distance from the wire, and μ₀ is the vacuum permeability, 4π×10&supminus;&sup7; T·m/A — conveniently, μ₀/(2π) simplifies to exactly 2×10&supminus;&sup7;, giving the more compact working form B = (2×10&supminus;&sup7; × I)/r. Magnetic field strength is measured in tesla (T), a unit adopted internationally in 1960 and named for Serbian-American engineer Nikola Tesla.

The field's direction follows the real right-hand rule: point your right thumb in the direction of conventional current flow, and your curled fingers show the direction the magnetic field circles around the wire.

Worked Example: Field Around a Current-Carrying Wire

What is the magnetic field 5 cm (0.05 m) from a wire carrying 10 A?

For comparison, Earth's own real surface magnetic field is roughly 25–65 µT — this ordinary current-carrying wire produces a field of genuinely comparable strength, just a few centimetres away.

Force on a Moving Charge

A charge moving through a magnetic field experiences a real, distinctive force — one that acts perpendicular to both the charge's own velocity and the field itself, a genuine structural difference from every force this course has covered so far:

(for velocity perpendicular to the field), with the exact direction given by a second real right-hand rule: point fingers along v, curl toward B, and the thumb gives the force direction on a positive charge.

Worked Example: Force on a Moving Charge

A charge of +2 µC moves at 1,000 m/s perpendicular to a 0.5 T magnetic field. What force does it feel?

Force on a Current-Carrying Wire

Since a current is simply many moving charges, a current-carrying wire sitting in a magnetic field feels a real, measurable force too:

where L is the length of wire within the field. This is exactly the real mechanism behind Chapter 3's own Ampère's force law — each of two parallel current-carrying wires sits inside the magnetic field the other wire creates (using this chapter's own B = μ₀I/(2πr) formula), and each therefore feels a force via F = BIL, attracting or repelling depending on whether the two currents flow in the same or opposite directions.

Worked Example: Force on a Wire

A 0.3 m length of wire carrying 5 A sits in a 0.2 T magnetic field, perpendicular to it. What force does the wire feel?

Electric vs. Magnetic Forces: A Real Structural Difference

Hands-On Exercises

Next chapter: Electromagnetic Induction (Faraday's Law) — where this chapter's own motor mechanism runs in reverse, and a changing magnetic field generates an electric current instead of the other way around.