Introductory Physics Volume Two

4.2 Magnetic Force on a Current 81
4 Magnetic Fields
§ 4.1 Magnetic Field
We have all played with magnets at some point. Magnets will
attract some types of metals and can attract and repel other magnets.
This seems similar to electric forces. Magnetic forces can indeed be
explained in terms of magnetic fields, but the connection between the
magnetic field and the magnetic force is significantly different from
that for electric fields and force. The magnetic field is similar to the
electric field in that they are both vector fields. We use the symbol B ⃗ to
represent the magnetic field. If we put a compass needle in a magnetic
field, the field will turn the needle until it is aligned with the direction
of the field. At this point we will use the following simple operational
definition of the magnetic field. The direction of the magnetic field
is the direction that a compass needle points. The magnitude of the
magnetic field is related to how strong the force is that aligns the needle
with the direction of the field.
A magnetic field does apply a force to charged particles. The
magnetic force on the particle has the following properties:
• F ∝ q
• F ∝ v
• F ∝ B
• F ⃗ is perpendicular to both ⃗v and B. ⃗ These can be combined into the
following succinct formula for the force.
Fact: Magnetic Force
A particle with charge q and velocity ⃗v in a magnetic field ⃗ B will
feel a force
⃗F = q ⃗v × ⃗ B
Notice that there is no force if the velocity is parallel to the magnetic
field. Also notice that the magnetic force is zero on a stationary
particle.