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Magnetic Fields
CHAPTER OUTLINE
29.1 Magnetic Fields and Forces
29.2 Magnetic Force Acting on a
Current-Carrying Conductor
29.4 Motion of a Charged Particle
in a Uniform Magnetic Field
29.5 Applications Involving
Charged Particles Moving in a
Magnetic Field
29.1 Magnetic Fields and Forces
Experiments on various charged particles moving in a magnetic field give the
following results:
We can summarize these observations by writing the magnetic force in the form
Right-hand rules for determining the direction of the magnetic force
The magnitude of the magnetic force on a charged particle is
FB is zero when v is parallel or antiparallel to B (Ɵ= 0
or 180°) and maximum when v is perpendicular to B
(Ɵ= 90°).
The SI unit of magnetic field is the newton per
coulomb-meter per second, which is called the tesla (T):
Example 29.1 An Electron Moving in a Magnetic Field
(B) Find a vector expression for the magnetic force on the electron
29.2 Magnetic Force Acting on a Current-Carrying Conductor
The direction of magnetic field
Magnetic field lines coming out of
the paper are indicated by dots,
representing the tips of arrows
coming outward.
Magnetic field lines going into
the paper are indicated by crosses,
representing the feathers of arrows
going inward.
Magnetic Force Acting on a Current-Carrying Conductor
considering a straight segment of wire of length L and crosssectional area A, carrying a current I in a uniform magnetic field B,
as shown in Figure. The magnetic force exerted on a charge q
moving with a drift velocity vd is
nAL is the number of charges in the segment.
We can write this expression in a more convenient form by noting that,
from Equation 27.4, the current in the wire is I = nqvdA. Therefore,
where L is a vector that points in the direction of the current I and has a
magnitude equal to the length L of the segment. Note that this expression applies
only to a straight segment of wire in a uniform magnetic field.
Example 29.2 Force on a Semicircular Conductor
A wire bent into a semicircle of radius R forms a closed circuit and
carries a current I. The wire lies in the xy plane, and a uniform
magnetic field is directed along the positive y axis, as shown in Figure.
Find the magnitude and direction of the magnetic force actingon the
straight portion of the wire and on the curved
portion.
The magnetic force F acting on the straight
portion has a magnitude F = ILB = 2IRB
because L = 2R.
29.4 Motion of a Charged Particle in a Uniform
Magnetic Field
consider a positively charged particle moving in a uniform magnetic field
with the initial velocity vector of the particle perpendicular to the
field. Let us assume that the direction of the magnetic field is into the
page, as in Figure. As the particle changes the direction of its velocity in
response to the magnetic force, the magnetic force remains perpendicular
to the velocity. If the force is always perpendicular to the velocity, the
path of the particle is a circle.
r is the radius of the path
the radius of the path is proportional to the linear momentum mv of
the particle and inversely proportional to the magnitude of the charge
on the particle and to the magnitude of the magnetic field. The angular
speed of the particle is
The period of the motion (the time interval the particle requires to
complete one revolution) is equal to the circumference of the circle
divided by the linear speed of the particle:
Example 29.6 A Proton Moving Perpendicular to
a Uniform Magnetic Field
Example 29.7 Bending an Electron Beam
29.5 Applications Involving Charged Particles
Moving in a Magnetic Field
A charge moving with a velocity v in the presence of both an
electric field E and a magnetic field B experiences both an electric
force qE and a magnetic force q vx B. The total force (called the
Lorentz force) acting on the charge is