Magnetic Fields

A fridge magnet’s grip, a compass swinging to north, the pull around a wire carrying current — all the same invisible thing: a magnetic field. And here’s the twist that ties this whole topic together: moving charge makes magnetism. Let’s map these fields and learn the rules that predict their direction.

What Makes a Magnetic Field

A magnetic field is any region where a magnetic pole would feel a force. There are two ways to make one:

• Permanent magnets — materials that produce a field all by themselves.
• Moving charge — an electric current. This is why a current-carrying wire has a magnetic field around it: the moving electrons create it. A charge sitting still produces no magnetic field.

The field itself is invisible, but we can detect it by the force it exerts on magnetic materials like iron, or by watching a plotting compass swing. A magnetic field is sometimes called a B-field.

Magnetic Field Lines

Just like electric fields, we draw magnetic fields with lines showing direction and strength. The direction rule here is: field lines always point from the north pole to the south pole. The simplest pattern is around a bar magnet.

The rules for drawing magnetic field lines mirror the electric ones: arrows point out of N and into S; the field is stronger where lines are closer and weaker where they’re further apart; and lines never cross.

Flux Density: How Strong Is the Field?

We measure magnetic field strength by how tightly packed the field lines are — the magnetic flux density, given the symbol B. It’s defined as the number of field lines passing through a region per unit area, and its unit is the tesla (T). One tesla is a precise amount:

Two Magnets: Attract or Repel

Bring two bar magnets together and the poles decide what happens — the same “likes and opposites” pattern as electric charge:

When two opposite poles are held close and facing each other, the field between them becomes uniform — equally spaced, parallel lines running from the N pole to the S pole, exactly like the uniform field between charged parallel plates.

The Field Around a Current-Carrying Wire

Send a current through a straight wire and it wraps a magnetic field around itself: concentric circles centred on the wire. The circles are packed tightest near the wire (strongest field) and spread apart further out. To show which way the field points, we use the right-hand grip rule: point your right thumb along the (conventional) current, and your curling fingers show the direction the field circles.

To draw currents flowing into or out of the page, we use a handy shorthand: a dot (·) is current coming towards you (out of the page), and a cross (×) is current going away (into the page).

One important note: “current” here means conventional current (from + to −), not the direction the electrons actually drift. Get that backwards and your grip-rule answer comes out reversed.

Solenoids and Coils

Wind that wire into a coil — a solenoid — and the fields from all the loops add together to make a strong, tidy field. In fact, a current-carrying solenoid behaves almost exactly like a bar magnet: one end becomes a north pole, the other a south pole, with field lines emerging from N and looping back into S. Because you’re stacking many loops into a small space, adding more turns (or more current) makes the field stronger — that’s how an electromagnet works.

A single flat circular coil is just one loop of a solenoid: the field lines pass through the middle, out of one face (a N pole) and into the other (a S pole). And on Earth, the whole planet acts like a giant bar magnet — which is why a compass needle’s north end swings to point at the Earth’s magnetic south pole, near the geographic North Pole.