Chapter 31
The Magnetic Field
31.1 Magnetic Field.
Recall how we defined the electric fieldEin Chapter 16: we place a small positive test chargeqat a point in
space, measure the forceFon it, and then compute the electric field as the force per unit charge:EDF=q.
We can similarly define amagnetic fieldBby measuring the forceFon a smallNmagnetic poleq; then the
magnetic field is defined as the force per unit pole strength:
BD
F
q: (31.1)
In SI units, the magnetic fieldBis measured in units ofteslas(T), named for the Serbian physicist Nikola
Tesla. One tesla is equal to 1 N A^1 m^1. A tesla is a very large unit; the largest magnetic fields that can
be produced in the laboratory are on the order of a few teslas. A common unit for working with terrestrial
magnetic fields is the nanotesla (nT). Another common unit ofBis thegauss(G), named for the German
mathematician Carl Friedrich Gauss. One gauss is equal to 10 ^4 tesla.
31.2 Magnetic Field due to a Single Magnetic Pole
The magnetic field due to a single magnetic poleqcan be found by using magnetic version of Coulomb’s
law. Let’s put a smallNpoleq 0 at some distancerfrom the poleq; then by the magnetic Coulomb’s
law, the force onq 0 isFD. 0 =4/.qq 0 =r^2 /. Dividing byq 0 gives us the magnetic field due to a single
magnetic poleq:
BD
0
4
q
r^2: (31.2)
Remember, though, that magnetic poleneveroccur in isolation—they only occur inN-Spolepairs.
31.3 Magnetic Field Lines
To help visualize the shape of the magnetic field, in can be helpful to draw diagrams ofmagnetic field lines,
similar to the electric field lines we drew earlier. These lines have the following properties:
- The magnetic field lines are directed lines (with arrows) that pointfromtheNpoletotheSpole.
- At any point along a field line, the magnetic field vectorBis tangent to the field line.