Magnetic Fields

What Is a Magnetic Field?

A magnetic field is a vector field that exerts a force on moving electric charges and magnetic dipoles. Unlike an electric field, which exerts forces on all charges (whether moving or stationary), a magnetic field only affects moving charges or aligned magnetic moments. Magnetic fields are generated by moving charges (electric currents) and by the intrinsic magnetic moments of particles and atoms.

Magnets always have two poles: north and south. Unlike electric charges, magnetic monopoles (isolated north or south poles) do not exist. Cutting a bar magnet in half does not separate the poles; instead, you get two smaller magnets, each with north and south poles. This is a fundamental asymmetry between electricity and magnetism rooted in the non-existence of magnetic monopoles.

Magnetic fields have both magnitude and direction. Field lines exit from the north pole and enter the south pole. The density of field lines indicates the magnitude. Unlike electric fields, magnetic field lines form closed loops (there are no sources or sinks of magnetic field).

Magnetic fields are ubiquitous in nature and technology. The Earth's magnetic field protects us from solar radiation. Magnets hold motors together, power electric generators, enable MRI medical imaging, and focus particle beams in accelerators. The magnetic field is one of the fundamental forces shaping the universe.

The Mathematics: The Lorentz Force and Ampère's Law

The foundation of magnetism is the Lorentz force, which describes the force a magnetic field exerts on a moving charge.

The key feature is the cross product: the force is perpendicular to both the velocity and the magnetic field. A charged particle moving perpendicular to a uniform magnetic field follows a circular path, as the magnetic force continuously redirects it. This principle is used in cyclotrons and other particle accelerators to keep particles in circular orbits.

The magnetic field is generated by electric currents. The quantitative relationship is given by Ampère's law:

Ampère's law states that the line integral of the magnetic field around a closed loop is proportional to the current passing through the loop. This law is one of Maxwell's equations and is equivalent to the Biot-Savart law, which gives the magnetic field from a specific current configuration.

This formula explains how motors work: a current-carrying wire in a magnetic field experiences a force perpendicular to both the current direction and the field, causing the wire to move.

Types of Magnetism

Ferromagnetism

Ferromagnetism is the strong, permanent magnetism exhibited by materials like iron, cobalt, and nickel. In ferromagnetic materials, the magnetic moments of electrons within atoms tend to align parallel to each other, even in the absence of an external field. This alignment creates significant spontaneous magnetization. Ferromagnetic materials can be magnetized and retain magnetism. They are characterized by high permeability (they greatly amplify applied magnetic fields) and exhibit hysteresis (magnetization depends on the history of applied fields).

Paramagnetism and Diamagnetism

Paramagnetic materials (aluminum, oxygen, many transition metals) have unpaired electrons with magnetic moments. In an external magnetic field, these moments tend to align with the field, weakly enhancing it. The effect is temporary—it disappears when the field is removed.

Diamagnetic materials (copper, water, most organic compounds) have no unpaired electrons. When placed in a magnetic field, the field induces magnetic moments that oppose the applied field, weakly repelling it. All materials exhibit diamagnetism; it is masked in paramagnetic and ferromagnetic materials by their stronger magnetic properties.

Antiferromagnetism

In antiferromagnetic materials (iron oxide, manganese oxide), atomic magnetic moments align antiparallel to each other, canceling out at the macroscopic level. These materials exhibit no net magnetization, though their magnetic structure is important for their properties.

Solenoids and Earth's Magnetic Field

Solenoids

A solenoid is a coil of wire carrying a current. The current creates a magnetic field that extends both inside and outside the coil. Inside a long solenoid, the field is approximately uniform and parallel to the axis. This simple configuration is extraordinarily useful for creating controlled magnetic fields in laboratory equipment, electromagnets, and countless applications.

The magnetic field inside a solenoid is B = μ₀ n I, where n is the number of turns per unit length and I is the current. By varying the current, we can control the field strength. Electromagnets using solenoid coils are far more practical than permanent magnets in many applications because we can turn them on and off and adjust their strength.

Earth's Magnetic Field

Earth has a powerful magnetic field extending far into space. The field is approximately that of a dipole, with the north magnetic pole currently located in the Canadian Arctic (and slowly drifting). The origin of Earth's magnetic field is the movement of liquid iron in the outer core, driven by heat from radioactive decay and primordial heat from Earth's formation.

The magnetic field strength at Earth's surface is about 25–65 microtesla (μT), varying with location. The field provides crucial protection against solar wind and cosmic rays by deflecting charged particles into the magnetosphere. Without this protection, solar radiation would strip away the atmosphere. The field also causes compass needles to point north and is essential for animal navigation.

Earth's magnetic field reverses polarity every few hundred thousand years on average. During reversals, the field weakens to very low values before reorienting with opposite polarity. These reversals are recorded in the magnetization of rocks and have been crucial in developing the theory of plate tectonics.

Historical Context

Magnetism has been known since ancient times. Magnetite, a naturally occurring magnetic iron ore, was discovered and used in early compasses. Chinese navigation compasses appeared by the 11th century. However, the scientific understanding of magnetism developed slowly.

For centuries, magnetism and electricity were treated as separate phenomena. The crucial breakthrough came in 1820 when Hans Christian Ørsted discovered that an electric current deflects a compass needle—electricity and magnetism are connected. Shortly after, André-Marie Ampère and others developed the quantitative laws governing magnetic fields from currents.

Michael Faraday discovered the reverse: a changing magnetic field induces an electric field and current (electromagnetic induction), demonstrating the deep reciprocity between electricity and magnetism. James Clerk Maxwell unified these phenomena into four equations (Maxwell's equations) showing that electricity and magnetism are two aspects of a single force: electromagnetism.

The 20th century saw the development of quantum mechanics, which explained magnetism at the atomic level through electron spin and orbital angular momentum. This understanding enabled the design of new magnetic materials and devices. Modern applications like MRI, superconducting magnets, and particle accelerators would be impossible without deep understanding of magnetism.

Real-World Applications

Electric Motors

Electric motors use the Lorentz force on current-carrying wires in a magnetic field. A coil of wire carrying current in a magnetic field experiences a torque, causing rotation. By continuously switching the current direction (commutation), the torque is maintained, producing sustained rotation. Motors power everything from household appliances to industrial machinery.

Electric Generators

Generators do the reverse: moving a coil of wire through a magnetic field induces an electric current (electromagnetic induction). Large generators powered by water flow (hydroelectric), steam (thermal power plants), wind, or other sources convert mechanical energy into electrical energy.

Transformers

Transformers use electromagnetic induction to convert between voltage levels. A primary coil generates a time-varying magnetic field that induces current in a secondary coil. By adjusting the number of turns, we can step voltages up or down. The entire power distribution system relies on transformers to efficiently transmit electricity over long distances at high voltages.

MRI (Magnetic Resonance Imaging)

MRI machines use powerful magnetic fields (typically 1.5–3 Tesla) to align nuclear spins in the body. Radiofrequency pulses excite the spins, and when turned off, the spins relax and emit detectable signals. The spatial encoding of these signals produces detailed internal images without ionizing radiation.

Particle Accelerators

Magnetic fields bend charged particles into circular paths, enabling cyclotrons and synchrotrons to accelerate particles to high energies. The Large Hadron Collider uses superconducting magnets to bend and focus particle beams.

Navigation and Magnetometry

Compass needles align with Earth's magnetic field, providing navigation. Modern magnetometers measure magnetic fields for mineral exploration, archaeological surveys, and diagnostic purposes.