Chapter 29 - Magnetic Fields
AA PowerPoint
PowerPoint Presentation
Presentation by
by
Paul
Paul E.
E. Tippens,
Tippens, Professor
Professor of
of Physics
Physics
Southern
Southern Polytechnic
Polytechnic State
State University
University
©
2007
Objectives: After completing this
module, you should be able to:
• Define the magnetic field, discussing
magnetic poles and flux lines.
• Solve problems involving the
magnitude and direction of forces on
charges moving in a magnetic field.
• Solve problems involving the magnitude
and direction of forces on current
carrying conductors in a B-field.
Magnetism
Since ancient times, certain materials, called
magnets, have been known to have the property of
attracting tiny pieces of metal. This attractive
property is called magnetism.
S
Bar Magnet
S
N
N
Magnetic Poles
Iron
filings
N
The strength of a magnet is
concentrated at the ends,
called north and south
“poles” of the magnet.
S
A suspended magnet:
N-seeking end and
S-seeking end are N
and S poles.
W
N
S
N
Bar magnet
S
N
E
Compass
Magnetic Attraction-Repulsion
S
S
N
N
N
Magnetic Forces:
Like Poles Repel
S
S
N
N
S
Unlike Poles Attract
Magnetic Field Lines
We can describe
magnetic field lines
by imagining a tiny
compass placed at
nearby points.
The direction of the
magnetic field B at
any point is the same
as the direction
indicated by this
compass.
N
S
Field B is strong where
lines are dense and weak
where lines are sparse.
Field Lines Between Magnets
Unlike
poles
Attraction
N
S
Leave N
and enter S
N
Like poles
N
Repulsion
The Density of Field Lines
Electric field
N
Magnetic field flux lines

B
A
A
S
Line density
N
E
A
A

N
Line density
Magnetic Field
Field BB isis sometimes
sometimes called
called the
the flux
flux
Magnetic
density in
in Webers
Webers per
per square
square meter
meter (Wb/m
(Wb/m22).).
density

Magnetic Flux Density
• Magnetic flux lines are
continuous and closed.

B
A
A

• Direction is that of the B
vector at any point.
• Flux lines are NOT in
direction of force but .
When
When area
area AA isis
perpendicular
perpendicular to
to flux:
flux:
Magnetic Flux
density:

B  ;  = BA
A
The unit of flux density is the Weber per square meter.
Calculating Flux Density When
Area is Not Perpendicular
The flux penetrating the
area A when the normal
vector n makes an angle
of  with the B-field is:
  BA cos
n
A


B
The angle is the complement of the angle a that the
plane of the area makes with the B field. (Cos  = Sin 
Origin of Magnetic Fields
Recall that the strength of an electric field E was
defined as the electric force per unit charge.
Since no isolated magnetic pole has ever been
found, we can’t define the magnetic field B in
terms of the magnetic force per unit north pole.
We
We will
will see
see instead
instead that
that
magnetic
magnetic fields
fields result
result from
from
charges
charges in
in motion—not
motion—not from
from
stationary
stationary charge
charge or
or poles.
poles.
This
This fact
fact will
will be
be covered
covered later.
later.
E
+
+
v
Bv
Magnetic Force on Moving Charge
Imagine a tube that
projects charge +q
with velocity v into
perpendicular B field.
Experiment shows:
F  qvB
F
B
v
N
S
Upward magnetic force F
on charge moving in B field.
Each of the following results in a greater magnetic
force F: an increase in velocity v, an increase in
charge q, and a larger magnetic field B.
Direction of Magnetic Force
The right hand rule:
With a flat right hand,
point thumb in direction
of velocity v, fingers in
direction of B field. The
flat hand pushes in the
direction of force F.
F
B
v
N
F
B
v
S
The
The force
force isis greatest
greatest when
when the
the velocity
velocity vv isis
perpendicular
perpendicular to
to the
the BB field.
field. The
The deflection
deflection
decreases
decreases to
to zero
zero for
for parallel
parallel motion.
motion.
Force and Angle of Path
N
N
N
S
S
S
Deflection force greatest
when path perpendicular
to field. Least at parallel.
F  v sin 
F
v sin 

v
B
v
Definition of B-field
Experimental observations show the following:
F  qv sin 
or
F
 constant
qv sin 
By choosing appropriate units for the constant of
proportionality, we can now define the B-field as:
Magnetic Field
Intensity B:
F
B
qv sin 
or
F  qvB sin 
AA magnetic
magnetic field
field intensity
intensity of
of one
one tesla
tesla (T)
(T) exists
exists in
in aa
region
region of
of space
space where
where aa charge
charge of
of one
one coulomb
coulomb (C)
(C)
moving
-field will
moving at
at 11 m/s
m/s perpendicular
perpendicular to
to the
the BB-field
will
experience
experience aa force
force of
of one
one newton
newton (N).
(N).
Example 1. A 2-nC charge is projected with
velocity 5 x 104 m/s at an angle of 300 with a
3 mT magnetic field as shown. What are the
magnitude and direction of the resulting force?
Draw a rough sketch.
q = 2 x 10-9 C
v = 5 x 104 m/s
v sin 
B = 3 x 10-3 T
 = 300
F
B

v
B
v
Using right-hand rule, the force is seen to be upward.
F  qvB sin   (2 x 10-9C)(5 x 104 m/s)(3 x 10-3T) sin 300
-7
Resultant
Resultant Magnetic
Magnetic Force:
Force: FF == 1.50
1.50 xx 10
10-7 N,
N, upward
upward
Forces on Negative Charges
Forces
Forces on
on negative
negative charges
charges are
are opposite
opposite to
to those
those on
on
positive
positive charges.
charges. The
The force
force on
on the
the negative
negative charge
charge
requires
-hand rule
.
requires aa left
left-hand
rule to
to show
show downward
downward force
force FF.
Right-hand
rule for
positive q
N
F
B
v
S
Left-hand
rule for
negative q
N
B
F
v
S
Indicating Direction of B-fields
One way of indicating the directions of fields perpendicular to a plane is to use crosses X and dots  :
A field directed into the paper
is denoted by a cross “X” like
the tail feathers of an arrow.
















X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
A field directed out of the paper
is denoted by a dot “” like the
front tip end of an arrow.
Practice With Directions:
What
What isis the
the direction
direction of
of the
the force
force FF on
on the
the charge
charge in
in
each
each of
of the
the examples
examples described
described below?
below?
X
X
X
X
F
X X X
Up
v
X+ X X
X X X
X X X
X
X
Left
X
X




F
  
Up
v
  
 -  
negative q
  




v
X X
FX X
+
X X
X X
X
X
X
X
  
 F
Right
  
v
  
Crossed E and B Fields
The
The motion
motion of
of charged
charged particles,
particles, such
such as
as electrons,
electrons, can
can
be
be controlled
controlled by
by combined
combined electric
electric and
and magnetic
magnetic fields.
fields.
Note: FE on electron
is upward and
opposite E-field.
+
But, FB on electron is
down (left-hand rule).
Zero deflection
when FB = FE
e-
x x x x
x x x x
v
FE
E
--
e
B
v
B
FB
v
The Velocity Selector
This
This device
device uses
uses crossed
crossed fields
fields to
to select
select only
only those
those
velocities
velocities for
for which
which FFBB == FFEE.. (Verify
(Verify directions
directions for
for +q)
+q)
When FB = FE :
qvB  qE
E
v
B
Source
of +q
+
x x x x
x x x x
+q
v
-
Velocity selector
By
By adjusting
adjusting the
the EE and/or
and/or B-fields,
B-fields, aa person
person can
can
select
select only
only those
those ions
ions with
with the
the desired
desired velocity.
velocity.
Example 2. A lithium ion, q = +1.6 x 10-16 C,
is projected through a velocity selector where
B = 20 mT. The E-field is adjusted to select a
velocity of 1.5 x 106 m/s. What is the electric
field E?
Source
E
v
B
E = vB
of +q
+
x x x x
x x x x
+q
v
V
E = (1.5 x 106 m/s)(20 x 10-3 T);
44 V/m
EE == 3.00
x
10
3.00 x 10 V/m
Circular Motion in B-field
The
The magnetic
magnetic force
force FF on
on aa moving
moving charge
charge isis always
always
perpendicular
perpendicular to
to its
its velocity
velocity v.
v. Thus,
Thus, aa charge
charge moving
moving
in
in aa B-field
B-field will
will experience
experience aa centripetal
centripetal force.
force.
mv 2
; FB  qvB;
FC 
R
FC  FB
The
The radius
radius
of
of path
path is:
is:
Centripetal Fc = FB
2
mv
 qvB
R
mv
R
qB
+
X
X
+X
X
X
X
X
X
X FX
X
X
X
X
X
X
X
X
X
X
X
X
+
X
X X
R
X X
c
X
+
X
X
Mass Spectrometer
+q
slit
x
x
x
x
x
x
x
x
E
v
+ B
R
Photographic
plate
x x x x x x x x x
x x x x x x x x
x x x x x x x
x x x x x x
x x x x
mv 2
 qvB
R
m1
Ions passed through a
velocity selector at
known velocity emerge
into a magnetic field as
shown. The radius is:
mv
R
qB
m2
The mass is found by
measuring the radius R:
qBR
m
v
Example 3. A Neon ion, q = 1.6 x 10-19 C, follows
a path of radius 7.28 cm. Upper and lower B =
0.5 T and E = 1000 V/m. What is its mass?
+q
slit
E
v
+ B
xx
Photographic
xx
plate
xx
R
xx
x x x x x x x
x x x x x x x
x x x x x x x
m
x x x x x x
x x x x
E 1000 V/m
v 
B
0.5 T
v = 2000 m/s
mv
R
qB
(1.6 x 10-19 C)(0.5 T)(0.0728 m)
m
2000 m/s
qBR
m
v
-24
m
m == 2.91
2.91 xx 10
10-24 kg
kg
Summary
The
The direction
direction of
of forces
forces on
on aa charge
charge moving
moving in
in an
an electric
electric
field
-hand rule
field can
can be
be determined
determined by
by the
the right
right-hand
rule for
for positive
positive
charges
-hand rule
charges and
and by
by the
the left
left-hand
rule for
for negative
negative charges.
charges.
Right-hand
rule for
positive q
N
F
B
v
S
Left-hand
rule for
negative q
N
B
F
v
S
Summary (Continued)
F
v sin 

For a charge moving in a
B-field, the magnitude of
the force is given by:
v
B
v
F = qvB sin 
Summary (Continued)
The velocity
selector:
E
v
B
The mass
spectrometer:
mv
R
qB
qBR
m
v
+
+
vq
x x x
x x x
x x
-
V
+q
-
slit
xx
xx +
xx
xx
x x x
x x x
x x x
x x
E
v
B
R
x
x
x
x
x
x
x
x
x x
x x
x x
x m
CONCLUSION: Chapter 29
Magnetic Fields