Magnetic Fields and Forces: From Compass to MRI

Every Moving Charge Creates a Magnetic Field

A single electron drifting through a wire generates a magnetic field around it. Millions of electrons moving together create the fields that run electric motors, store data on hard drives, shield Earth from solar radiation, and image the interior of the human body. Magnetism and electricity are two faces of one force — electromagnetism — and understanding one requires understanding the other.

The Origin of Magnetic Fields

Magnetic fields arise from two sources: moving electric charges (currents) and the intrinsic spin of elementary particles. A current-carrying wire generates a circular magnetic field around itself, described by the right-hand rule: point your thumb in the current direction, and your curled fingers show the field direction.

Electron spin creates permanent magnetism in materials. In most substances, electron spins point randomly, canceling out. In ferromagnetic materials (iron, nickel, cobalt, and some alloys), quantum exchange interactions cause neighboring electron spins to align in domains. When domains align, the material becomes a permanent magnet.

Magnetic Field Strength

Magnetic field strength is measured in Tesla (T). To calibrate intuition:

The Lorentz Force

A charged particle moving through a magnetic field experiences the Lorentz force:

F = qv × B

The force is perpendicular to both the velocity (v) and the field (B). This means the magnetic force never speeds up or slows down a particle — it only changes direction. Charged particles spiral along magnetic field lines rather than following straight paths. This is why cosmic ray particles curve in Earth's magnetosphere and how mass spectrometers separate ions by mass.

• If charge is zero: no force
• If velocity is parallel to B: no force
• Maximum force: when velocity is perpendicular to B

Faraday's Law and Electromagnetic Induction

A changing magnetic field creates an electric field — this is Faraday's law. A wire loop moving through a magnetic field develops a voltage. This is the basis for:

• Generators — rotating coils in a magnetic field produce AC current
• Transformers — alternating current in one coil induces voltage in another through shared flux
• Induction cooking — alternating field induces currents directly in the pot, heating it
• Wireless charging — same principle, shorter range

Earth's Magnetosphere

Earth's liquid iron outer core flows in convection currents driven by heat from the inner core. This motion of conducting fluid generates Earth's geodynamo — a self-sustaining magnetic field. The magnetosphere extends roughly 10 Earth radii toward the Sun and millions of kilometers in the anti-solar direction (the magnetotail).

Without it, the solar wind would strip Earth's atmosphere. Mars lost most of its atmosphere partly because its magnetic field collapsed ~4 billion years ago. Earth's field has reversed hundreds of times in geological history (the last reversal was 780,000 years ago) and is weakening at about 5% per century — a change monitored carefully by geophysicists.

Magnetic Monopoles: The Missing Particle

Electric charges come alone — isolated positive or negative charges exist freely. Every magnetic dipole (north-south pair) you cut in half produces two smaller dipoles, never an isolated north or south pole. Magnetic monopoles — single poles — are forbidden by Maxwell's equations as currently written, though string theory and grand unified theories predict they should exist. None has ever been detected. Paul Dirac showed in 1931 that if even one magnetic monopole existed anywhere in the universe, it would explain why electric charge is quantized.

Applications of Magnetic Fields

Maxwell's four equations, published in 1865, unified electricity and magnetism into a single framework and predicted electromagnetic waves traveling at the speed of light — the discovery that light itself is an electromagnetic wave. That unification remains one of physics' greatest achievements.