Topic 12.1 Magnetic Fields: describe magnetic fields, their sources in moving charges and magnets, field-line representation, and the absence of magnetic monopoles.

What this topic is asking

The College Board (Topic 12.1) wants you to describe the magnetic field $\vec{B}$, recognize that its sources are moving charges and magnetic dipoles, represent it with field lines, and grasp the deep difference from the electric field: there are no magnetic monopoles, so field lines always close on themselves.

The magnetic field and its sources

The fundamental source of a magnetic field is moving charge: a current-carrying wire and even a single moving charge create one. Permanent magnets owe their fields to the aligned microscopic current loops of their atoms' electrons. A static charge produces only an electric field; it takes motion to make magnetism. This is a deep unification: electricity and magnetism are two aspects of one electromagnetic interaction, related by motion. What looks like a pure electric field to one observer can include a magnetic field to another moving relative to the first, a hint of the relativity that underlies Maxwell's equations.

Field lines and dipoles

Magnetic field lines show the field's direction (a compass needle aligns with them). Outside a magnet they run from the north pole to the south pole, then continue inside the magnet from south back to north, closing the loop. Every magnet is a dipole, with a north and a south pole that cannot be separated.

No monopoles, and Gauss's law for magnetism

This is the sharpest contrast with electricity, where isolated charges exist and electric field lines begin and end on them ($\oint\vec{E}\cdot d\vec{A} = q_{enc}/\varepsilon_0$). The two Gauss's laws, $\oint\vec{E}\cdot d\vec{A} = q_{enc}/\varepsilon_0$ and $\oint\vec{B}\cdot d\vec{A} = 0$, are two of the four Maxwell equations that summarize all of electromagnetism; the difference between them, charge versus no monopole, is exactly the asymmetry that makes electric field lines terminate but magnetic field lines close. Searches for magnetic monopoles continue, but none has ever been confirmed, so $\oint\vec{B}\cdot d\vec{A} = 0$ stands as an experimental law.

Try this

Q1. State the SI unit of magnetic field. [1 point]

• Cue. The tesla (T).

Q2. Explain why the net magnetic flux through a closed surface is zero. [2 points]

• Cue. Magnetic field lines form closed loops (no monopoles), so every line entering the surface also leaves it.