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5.6.1. Magnetic Fields

Table of Contents

What a Magnetic Field Is

A magnetic field is a physical field that describes magnetic effects in space. It tells us how magnets, moving charges, and electric currents influence other moving charges and magnetic materials nearby. The magnetic field is usually represented by the symbol $\vec{B}$.

Unlike a simple number, a magnetic field has both size and direction, so it is a vector field. At each point in space, $\vec{B}$ points in the direction a small compass needle would try to align.

The magnetic field is denoted by $\vec{B}$ and is a vector quantity.
Its SI unit is the tesla, $\mathrm{T}$.

If you place a small magnet or compass near a bar magnet, the compass turns. This turning happens because the magnetic field exists in the region around the magnet. The field is invisible, but its effects are measurable.

Sources of Magnetic Fields

Magnetic fields are produced mainly by moving electric charges. In practice, this means electric currents create magnetic fields. Permanent magnets also produce magnetic fields, but at the microscopic level this comes from motion and intrinsic magnetic properties of electrons inside the material.

A charge that is standing still produces an electric field. A charge that is moving can produce both an electric field and a magnetic field. This is one of the key ideas of electromagnetism.

Common sources of magnetic fields include a straight current-carrying wire, a loop of current, a solenoid, and a permanent magnet. Detailed laws for calculating these fields belong to later chapters, but the central idea is simple, currents make magnetic fields.

How We Describe Direction

The direction of a magnetic field at a point is defined operationally. Imagine placing a very small compass at that point. The north-seeking end of the compass points along the direction of $\vec{B}$.

For a bar magnet, outside the magnet the magnetic field points from the north pole toward the south pole. Inside the magnet, the field returns from south to north, forming closed loops.

This is an important difference from electric field lines, which can begin and end on charges. Magnetic field lines do not begin or end at isolated magnetic charges.

Magnetic field lines form closed loops.
There are no isolated magnetic poles observed in ordinary physics, so magnetic field lines do not start or stop in empty space.

Magnetic Field Lines

Magnetic field lines are a visual tool used to represent the magnetic field. They are not physical strings in space, but they help us picture the field.

The tangent to a field line gives the direction of $\vec{B}$ at each point. Where the lines are closer together, the magnetic field is stronger. Where they are farther apart, the field is weaker.

For a bar magnet, the pattern curves outward from one end and back to the other. For a straight wire carrying current, the magnetic field lines form circles around the wire.

Magnetic field lines around a bar magnet

Uniform and Nonuniform Magnetic Fields

A magnetic field can be uniform or nonuniform. In a uniform magnetic field, the magnitude and direction are the same everywhere in a region. In drawings, uniform fields are often shown by parallel equally spaced field lines.

Near the center between large magnet poles, the field can be approximately uniform. Around a small magnet or wire, the field usually changes with position, so it is nonuniform.

Uniform fields are useful in simple problems because they make the motion of charged particles easier to analyze.

A uniform magnetic field

Units of Magnetic Field

The SI unit of magnetic field is the tesla, abbreviated $\mathrm{T}$. In many practical situations, fields may also be expressed in millitesla, $\mathrm{mT}$, or microtesla, $\mu\mathrm{T}$.

The Earth's magnetic field near the surface is relatively weak, about tens of microtesla. A strong laboratory magnet may produce fields of the order of tesla.

Magnetic field exampleTypical size
Earth's field$\sim 50\,\mu\mathrm{T}$
Small magnet near its surface$\sim 10^{-2}$ to $10^{-1}\,\mathrm{T}$
Strong lab magnet$\sim 1\,\mathrm{T}$ or more

The Earth as a Magnet

The Earth itself has a magnetic field. This is why a compass works outdoors. The field is roughly similar to that of a giant bar magnet, though the real structure is more complicated.

The Earth's magnetic field helps define geographic navigation directions, but magnetic north and geographic north are not exactly the same. A compass aligns with the local magnetic field, not directly with the rotation axis of Earth.

Distinguishing Magnetic Field from Magnetic Force

It is important not to confuse the magnetic field with the magnetic force. The field is the condition in space, while the force is the effect on an object placed in that field.

A magnetic field can exist in a region even if no test object is there. When a moving charge, a current-carrying wire, or a magnetic dipole is placed in that region, it may experience a force or a torque.

Later chapters will discuss the magnetic force in detail. For now, the key idea is that the field describes the magnetic environment.

Do not confuse these two ideas:
Magnetic field, $\vec{B}$, is a property of space.
Magnetic force is the effect on a moving charge, current, or magnet placed in that field.

A First Qualitative Rule

Although the exact force law is discussed later, one basic fact is useful here. Magnetic fields act most directly on moving charges, not on stationary charges.

A stationary electric charge does not experience magnetic force just because a magnetic field is present. Motion matters. This is one reason magnetic phenomena are deeply connected with electric currents.

Right Hand Rule for Field Around a Wire

For a straight wire carrying current, the magnetic field circles around the wire. The direction can be found with the right hand rule. Point your right thumb in the direction of the conventional current. Your curled fingers show the direction of the magnetic field lines.

This rule helps determine direction only. It does not by itself give the field strength.

Magnetic field around a straight current-carrying wire

Magnetic Fields and Materials

Some materials respond strongly to magnetic fields. Iron is a familiar example. A piece of iron placed near a magnet can itself become magnetized. Other materials respond weakly.

This chapter focuses on the field itself, not the detailed behavior of magnetic materials. What matters here is that a magnetic field can influence matter differently depending on the material.

Summary Picture

A magnetic field is a vector field represented by $\vec{B}$. It is produced by moving charges, currents, and magnets. Its direction is the direction a compass points, and its field lines form closed loops. Around a straight wire, the field forms circles. In a uniform region, the field has the same magnitude and direction everywhere. The SI unit is the tesla.

Essential facts about magnetic fields:
$\vec{B}$ is a vector field.
Magnetic fields are produced by moving charges and currents.
A compass aligns with the direction of $\vec{B}$.
Magnetic field lines form closed loops.
The SI unit of magnetic field is the tesla, $\mathrm{T}$.

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