A current is a stream of moving charge, and it makes a magnetic field that circles it. A long straight wire carrying 1 A makes 20 µT at 1 cm, about the Earth’s own field; the field falls off as 1 over the distance.
Outside it, a bar magnet is the same as a sheet of current running round its sides, and that is how it is drawn here. The lines leave at the north pole and return at the south, and they never start or stop.
The force on a moving charge is sideways to its motion, so it changes the direction and never the speed: the charge goes round a circle. The time for one turn depends on the field and the particle, not on how fast it goes.
Change the flux through a coil and a voltage appears, in proportion to the turns and to how fast it changes; the current it drives opposes the change. Nothing happens while the flux is steady.
The field of a long straight wire is μ0I/2πr, which is 2×10−7 times the current over the distance. So 1 A at 1 cm is as strong as the Earth’s field, 10 A at 10 cm the same again, and a wire carrying 20 A 1 cm from a compass will swing it.
A uniformly magnetised magnet of remanence Br acts like a surface current of Br/μ0 amperes per metre. For a neodymium cylinder 20 mm long and 20 mm across with Br = 1.3 T, the exact field on the axis is 0.58 T on the pole face and only 0.05 T 2 cm beyond it: a magnet’s field falls away much faster than a wire’s, as the cube of the distance far off. Its magnetic moment is 6.50 A m².
Inside a long solenoid the field is μ0nI with n the turns per metre: 1,000 turns a metre carrying 5 A gives 6.3 mT, uniform across the bore. Two coils one radius apart (Helmholtz) give a field at the centre of 0.7155 μ0NI/R, which is 9.0 µT for one turn of 10 cm radius carrying 1 A, and it changes by only 0.42 percent a quarter of a radius out; they are used to cancel the Earth’s field and to calibrate magnetometers.
A 100 eV electron in a field of 1 mT moves at 5.9 thousand km/s and goes in a circle of radius 3.4 cm, once every 36 ns. The turns per second, qB/2πm, depend on the field alone: 28.0 GHz for an electron in 1 T and 15.2 MHz for a proton, however fast either goes. That fixed beat is what a cyclotron uses to give a particle a push every half turn.
Accelerate ions through 3,000 V and turn them in 0.25 T, and each travels a semicircle of radius proportional to the square root of its mass. Carbon-12 turns in a circle of 10.9 cm and carbon-13, which is 8.4 percent heavier, in one 11.4 cm: they land 9.0 mm apart, enough to count them separately. The mass spectrometer is how isotopes were discovered, and how a forensic lab identifies a molecule.
Two long parallel wires 1 m apart, each carrying 1 A, pull on each other with 2.0×10−7 newtons for every metre of length. That was the definition of the ampere until 2019, and it is why the number μ0 used to be exactly 4π×10−7.
A magnet dropped down a copper tube takes many times longer to fall than through a plastic one. As it falls, the flux through each ring of the tube changes, which drives currents round the ring, and by Lenz’s law those currents oppose the fall, pushing up on the magnet below it and pulling down the one above. The voltage in the coil in the Induction section is the same effect, and its energy comes from the fall.
A coil of 100 turns and 100 cm² turning at 50 revolutions a second (3,000 rpm) in a field of 0.1 T makes a sine wave of peak NBAω = 31.4 V, which is 22.2 V RMS, the number a meter reads. Mains frequency is simply the speed at which the machine turns: 3,000 rpm for 50 Hz and 3,600 rpm for 60 Hz with one pair of poles, or half of those with two pairs.
The Earth’s field at the surface runs from about 22 to 67 µT, and the model on this page puts the declination, for late October 2026, in London at +1.2° (a compass points that far east of true north), in Sydney at +12.8°, in New York at -12.5° and in Reykjavik at -11.0°; a free needle dips 67° below the horizontal in London and 64° above it in Sydney. The field is made by currents in the liquid iron of the core, so it drifts, and the magnetic pole has been moving by tens of kilometres a year; the model is renewed every five years.
The coils and magnets are ideal: perfectly uniform windings and magnetisation, no iron cores, no saturation, no temperature effects, and no fields that change fast enough to radiate. The particle section ignores the particle’s own radiation. The Earth’s field is the main field of the World Magnetic Model, good to about half a degree of declination and valid from 2025 to the end of 2029; it leaves out the local field of rocks, steel and buildings, and the changes of the upper atmosphere in a magnetic storm, and it cannot be used for a compass within about 1,000 km of a magnetic pole.
Moving electric charge. A current in a wire makes one that circles the wire; a magnet makes one because the electrons in its atoms, spinning and orbiting, are lined up and their small fields add. There are no separate magnetic charges: a magnet cut in two always makes two magnets.
Because there are no magnetic monopoles, so the field has no sources or sinks. The lines are closed loops: outside a magnet they run from the north pole to the south pole and inside it they run on from south to north. Where they crowd, the field is strong.
A fridge magnet is about 5 mT on its surface, a neodymium magnet 0.5 to 1.3 T, an MRI scanner 1.5 to 3 T and the strongest steady laboratory magnet 45 T. The Earth’s field is 22 to 67 µT, about ten thousand times weaker than the surface of a neodymium magnet.
Because the force is always at right angles to the velocity. A force at right angles to the motion changes its direction but not its speed, so the particle’s kinetic energy stays the same. A magnetic field can bend a beam but not accelerate it; an electric field does that.
The ions are all given the same energy by a voltage, so a lighter one goes faster; then a magnetic field turns each in a circle of radius proportional to the square root of its mass over its charge. The radius tells you the mass, and where it lands is measured.
The current induced by a changing flux flows in the direction that opposes the change. Push a magnet towards a coil and the coil makes a field that pushes back; pull it away and it pulls back. It is conservation of energy: if it helped the change the system would gain energy from nothing.
Because a coil turning in a field has its flux going up and down as a cosine of the angle, and the voltage is the rate of change, a sine. It reverses each half turn. A commutator or a rectifier turns it into direct current if that is wanted.
Because it follows the Earth’s magnetic field, whose north pole is in the Arctic Ocean north of Siberia and moving, not the point the Earth spins about. The angle between them is the declination; it is zero along a wandering line and several degrees either side of it, and it changes year by year, which is why maps print it with a date.
Because the Earth’s field is not horizontal except near the magnetic equator: it leaves the ground in the southern hemisphere and enters it in the northern, as a bar magnet’s does. The dip, or inclination, is zero at the magnetic equator and 90° at the poles, and compasses for different regions are weighted to balance it.
It is the World Magnetic Model of the US National Centers for Environmental Information and the British Geological Survey, which predicts the main field to about half a degree of declination and 100 nT in strength for 2025 to 2029. It does not include the field of the rocks and metal at the exact spot.
This page has changed in 4 archived releases, but each of those was a site-wide pass, so none is attributable to this tool on its own and none is listed here. That is not a claim that the tool never changed — a release that reworked many pages at once may well have altered this one too. The changelog has them.