Ch 28 Magnetic Fields
2 What Produces a Magnetic Field? Individual magnetic monopoles do not exist. However, permanent
magnets and electromagnets, with positive and negative magnetic poles pairs, generate magnetic fields.
⃗ . (Recall the definition of the cross
3 The Definition of ⃗⃗ . Finding the magnetic force on a particle.
product, including the “right-hand rule.”) The force
acting on a charged particle moving with velocity
through a magnetic field ⃗ is always perpendicular to and ⃗ .
Units:
.
 Table 28-1. Some Approximate Magnetic Fields.
 Checkpoint 1
Magnetic field lines. These are defined in analogy to electric field lines, but due to the absence of magnetic
monopoles, they never terminate. Opposite magnetic poles attract each other, and like magnetic poles repel
each other. Note the “reversed” definition of geomagnetic poles.
 Sample Problem : Magnetic force on a moving charged particle
4 Crossed Fields: Discovery of the Electron. Given the right geometry, a velocity “selector” will pick out
particles with speed
.
 Checkpoint 2
6 A Circulating Charged Particle. If a particle moves with velocity perpendicular to a uniform magnetic field
⃗ , it will undergo uniform circular motion described by the relation
, where is the charge, m
is the mass, and is the path radius. Helical paths. If is not perpendicular to ⃗ , then the particle’s path is a
helix with axis ⃗ .
 Checkpoint 3
 Sample Problem: Helical motion of a charged particle in a magnetic field
 Sample Problem: Uniform circular motion of a charged particle in a magnetic field
8 Magnetic Force on a Current-Carrying Wire. If a straight wire segment of length
⃗
⃗ ⃗.
uniform magnetic field ⃗ , it will receive a force
 Checkpoint 4
 Sample Problem: Magnetic force on a wire carrying current
carries current in a
9 Torque on a Current Loop. The torque on a planar rectangular loop of wire, carrying current in the
presence of a uniform magnetic field ⃗ is
, where and are the lengths of the rectangle’s
sides, and is the angle between the field and the normal to the loop, using the right-hand rule.
10 The Magnetic Dipole Moment. For a current-carrying coil, the magnetic dipole moment has direction given
by the right-hand rule, and magnitude
, where is the number of loops in the coil, is the current in
each loop, and is the area of the coil. A magnetic dipole in an external magnetic field receives a torque
⃗ , and potential energy
⃗.
 Table 28-2: Some Magnetic Dipole Moments
 Checkpoint 5
 Sample Problem: Rotating a magnetic dipole in a magnetic field
----------------Material below is not covered in this course----------------------------------------------------5 Crossed Fields: The Hall Effect
7 Cyclotrons and Synchrotrons