A force you have felt your whole life
Stick a note to the fridge, watch a compass needle swing north, feel two magnets snap together or shove apart — magnetism is everywhere, yet completely invisible. It hides in your headphones, your hard drive, the motor of every fan, and the giant coils of an MRI scanner. This track will take you from that everyday tug all the way to the equations that describe light itself.
Play with two bar magnets and one rule emerges: like poles repel, unlike poles attract. Every magnet carries a north and a south pole — and no matter how you cut it, you never isolate just one.
The magnetic field: a map of magnetic influence
Rather than track pole-on-pole forces one by one, physicists describe the space around a magnet with a magnetic field \vec{B}: at every point it assigns an arrow giving the field's strength and direction. Scatter iron filings near a magnet and they line up along these directions, tracing the field lines. By convention the direction of \vec{B} is the way a tiny compass north-pole would point.
Outside a magnet the field lines run from north to south; inside they continue from south back to north, so every line closes on itself. Magnetic field lines never begin or end at a point. Contrast that with electric field lines, which sprout out of positive charges and die on negative ones.
Gauss's law for magnetism: the net magnetic flux through any closed surface is zero — a mathematical way of saying there are no isolated magnetic poles.
Field strength is measured in teslas (T); an older unit, the gauss (G), equals 10^{-4} T. For honest scale: the Earth's field is about 50\,\mu\text{T}, a fridge magnet a few mT, a strong lab magnet or MRI $1$–$3$ T, and the surface of a magnetar (a neutron star) can reach 10^{8}–10^{11} T.
One tesla is a large field: it defines how hard a field pushes on a moving charge, which we quantify in the next guide.
Oersted's shock: electricity makes magnetism
In 1820 Hans Christian Ørsted, lecturing to students, noticed that a compass needle jumped whenever he switched on a nearby current. A wire carrying charge deflects a compass just like a magnet does. The conclusion changed physics forever: electric currents produce magnetic fields. Magnetism is not a separate mysterious substance — it is what moving charge does.
So what makes a permanent magnet magnetic, if there is no current wire inside? The answer is the same: countless atomic-scale current loops — electrons circulating and, above all, their intrinsic spin — behave like tiny magnets. In iron these align, and the whole bar becomes a magnet. Electricity and magnetism turn out to be two sides of one coin, a unity we will complete at the end of this track.
The road ahead
Here is the arc of this track. Next we find the force a field exerts on a single moving charge — the Lorentz force. Then we watch that force bend charges into circles and grip whole current-carrying wires. After that we turn the question around and compute the fields that currents create, from the Biot–Savart law to Ampère's law and the solenoid. Finally we assemble everything into the torque on a loop (the electric motor), explain why iron is magnetic, and glimpse how these laws give birth to light. Let's begin.