Download Chapter 27: Magnetic Forces

Chapter 27: Magnetic Forces
•  In this chapter we study a new force associated with charged
particles, called the magnetic force.
•  This force is associated with charged particles moving with respect
to each other.
•  This force is broken into two parts: (1) moving charges produce
a magnetic field, and (2) particles moving in a magnetic field
experience a magnetic force.
Permanent Magnets
•  Some solid objects, due to the element it is made of
(which determines the number of valence electrons), are
permanent magnets.
•  If a bar magnet is taped to a piece
of cork and allowed to float in a
dish of water, it always turns to
align itself in an approximate
north-south direction (due to
Earth’s magnetic field).
•  The end of a magnet that points
north is called the north-seeking
pole, or simply the north pole. The
other end is the south pole.
Permanent magnets
•  Permanent magnets can be
attracted or repelled by other
magnets:
•  Like poles repel and opposite
poles attract.
•  Like the Earth’s magnetic field,
a bar magnet can cause a
compass to rotate.
Magnetic Fields
•  We define the direction of the magnetic field to be the
direction that the north pole of the compass points.
Experiments:
A permanent magnet will
attract some metals like iron
with either the north or south
pole.
No magnetic force on
plastics, copper, aluminum,
or glass materials.
+Q
Other than the weak electric
force due to charge separation,
the stationary charged-object
has no effect on the magnet.
Moving charges
in a magnetic
field experience
a magnetic
force.
What do these experiments tell us?
•  Magnetism is not the same as the electric force. They
have some similarities, but they are not the same.
•  Magnets have two poles, called north and south poles,
and thus are magnetic dipoles. Like poles repel, and
opposite poles attract.
•  Materials that are attracted to a magnet are called
magnetic materials (like iron). Magnetic materials are
attracted to either pole of a magnet.
•  Similar to the electric polarization force, but the difference is
that only a few materials are attracted to a magnet.
•  The goal of this and the next chapter is to explain these
and other observations.
Magnetic force
~ , exerts a force on
•  The magnetic field, designated B
moving charged particles.
•  The magnetic force on a moving
point-charge is given by:
~
F~ = q~v ⇥ B
F = |F~ | = qvB sin
A proton (q=+e) is released from rest in a uniform E
field and a uniform B field. The E field points up and
the B field points into the page. Which of the paths will
the proton follow?
C
A
D
B
E. It will remain stationary
Clicker Question
A proton beam enters a
magnetic field region as
shown below. What is
the direction of the
magnetic field B?
1) + y
2) – y
3) + x
4) + z (out of page)
5) – z (into page)
y
x
Motion of a charged particle in a uniform
magnetic field
~
F~ = q~v ⇥ B
•  Since the magnetic force is always at right angles to a charged
particle’s velocity…
•  A particle moving in a plane
perpendicular to the field undergoes
uniform circular motion.
•  orbital motion:
2
mv?
= qv? B
r
mv?
•  Cyclotron radius: r =
qB
•  If velocity has a component along B field: spiral motion.
•  Orbital radius still given by
mv?
r=
qB
positron
Invisible
Highenergy
photon
B
More energetic e+ epair
electron
Scattered atomic
electron
Mass spectrometer
velocity selector:
⇣
⌘
F =q E+v⇥B =0
E
v=
B
mv
mE
r=
=
qB
qB 2
Cyclotron Particle Accelerator
•  The cyclotron
frequency:
v
qB
f=
=
2 r
2 m
•  independent of
the particle’s
speed
•  Voltage difference across
gap oscillates at cyclotron
frequency, so particle is
accelerated twice each
orbit.
•  Particle spirals outward
and then escapes
The magnetic force on a current-carrying wire
•  An electric current consists of moving charges, so a currentcarrying conductor experiences a magnetic force equal to the
summation of all the individual forces of each moving particle.
Force on wire chunk of length L:
F = (nAL)(qv ⇥ B)
F = (qnvAL) ⇥ B
F = (JAL) ⇥ B
~ ⇥B
~
F~ = I L
CT 32.7b
A current-carrying wire is in a B-field.
What is the direction of the magnetic force on
the wire?
A:
B:
C:
B
D:
E: Other/not sure
©University of Colorado, Boulder (2008)
i
•  More generally, if the wire isn’t in a straight line and/or if
the magnetic field is not uniform, the net force is
determined by integration:
F~ =
Z
~ ⇥B
~
I dl
Clicker Question
Magnetic Fields Exert Torques on Current Loops
⌧ = 2Ftop r? = 2(ILB)(L/2 sin ✓)
⇥ = IBA sin( ) = µB sin( )
~
) ~⌧ = µ
~ ⇥B
•  A current of I = 2 A runs through the current loop, as
shown below. What magnetic field strength is required to
prevent the current loop from rotating about the axle?
The Electric Motor
http://www.walter-fendt.de/ph14e/electricmotor.htm
Slide 24-43
CT 33.7c
An electric motor consists of a coil, free to turn
on an axis, in an magnetic field created by
permanent magnets.
Which way will the coil shown rotate?
B
B
I
A)
CW
CCW
B)
C) It won’t rotate in this configuration
toyota hybrid motor
disk drive motor
Clicker question
•  In what direction is the net magnetic force on the current
loop (current is counter-clockwise as seen from above)?
S
N
far side
1.  up
2.  down
3.  zero
4.  none of the above
I
near side
Loudspeaker engineering
•  To create music, we need longitudinal pulses in the air. The speaker
cone is a very clever combination of induced and permanent
magnetism arranged to move the cone to create compressions in the
air.
Hall Effect
VH = Et = Bvt