Download The magnetic field due to the long horizontal wire points straight up

Chapter 20
Magnetism
© 2006, B.J. Lieb
Some figures electronically reproduced by permission of Pearson
Education, Inc., Upper Saddle River, New Jersey Giancoli,
PHYSICS,6/E © 2004.
Ch 20
1
Magnets
•Occur naturally in some parts of the world.
•Each magnet has two faces called “poles”
•A magnet suspended freely becomes a compass
•The end of the compass that points toward the earth’s
geographic north pole is called the north pole of the
magnet.
•The other pole points to the south and is called the
south pole.
•For magnets, unlike poles attract but don’t confuse with
electric charge:
S
N
N
S
N
Ch 20
S
N
S
Repulsive
S
N
Repulsive
N
S
Attractive
2
Magnetic Fields
•Magnetic field symbolized by letter B
•B is measured in tesla (T) or gauss (G)
•1G = 10-4 T
•Direction determined by direction the north end of a
magnet points.
•Points out of north pole and into south pole.
Ch 20
3
Magnetic Field of Earth
North

•Earth’s magnetic field is not due to a permanent magnet– appears
due to molten iron core and earth’s rotation.
•North geographic pole is a south magnetic pole
•Magnetic field lines are not parallel to surface
•Angle of dip θ: angle the field makes with horizontal.
Ch 20
4
Electric Currents Produce Magnetic Fields
•A wire carrying a current produces a magnetic field which
circles wire as shown
•Right hand rule: grasp wire such that thumb points in
direction of current, fingers give magnetic field direction.
Ch 20
5
Magnetic Field of Long Straight Wire
0 I
B 
2 r
•I is current in wire
• r is distance from wire
•0 is permeability of free space
•0 = 4 x 10-7 T m / A
Ch 20
6
Example 20-1. A long horizontal wire carries 22.0 A of current due north. What
is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there
points north but downward, 37° below the horizontal, and has magnitude
5.0x10-5 T.
The magnetic field due to the long horizontal wire points straight up at the
point in question. The wire would be parallel to the red line shown and outside
the page. The two fields are oriented as shown in the diagram. The net field is
the vector sum of the two fields.
0 I
Bwire 
2 r
B
4 10

T m / A(22.0 A)
 2.2  105 T
2 (0.200 m)
7
 5.0  10 T
5
earth

Bwire

South

Bearth
Ch 20

Bnet
North
7
Example 20-1. Continued A long horizontal wire carries 22.0 A of current due
north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s
field there points north but downward, 37° below the horizontal, and has

magnitude 5.0x10-5 T.
B
wire

South

Bearth
B B
net x
B
net y
earth
wire
net
2
net x
earth
sin 37    0.81  10 5 T
 B  (4.00  10 T)  (0.81  10 T)  4.1  10 T
5
2
2
5
5
2
net y
B
  tan
B
Ch 20
1
North
cos 37   4.00  10 5 T
B B
B  B

Bnet
net y
net x
 0.81  10 T

 11
 tan
4.00  10 T
5
1
5
below the horizontal
8
Magnetic Field of Long Straight Wire
X
X
X
X
X
X
X
X
X
X
X
X
This drawing represents the magnetic field of a wire carrying a current
directed upward. The wire is in the plane of the screen and the magnetic
field is shown in the plane of the screen The dots to the left of the wire
represent a magnetic field directed out of the screen and the X’s to the
right of the wire represent a magnetic field into the screen.
Ch 20
9
Magnetic Field of Current Loop
•A loop of wire carrying a current has a magnetic field
similar to a bar magnet.
•Many loops produce a strong uniform field in the center
and this is referred to as a solenoid.
Ch 20
10
Magnetic Force on Moving Charge
•If electric current exerts a force on a compass, we expect
magnetic field exerts a force on current-carrying wire
(Newton’s Third Law)
•Second Right Hand Rule: orient outstretched fingers in
current direction and bend them to field direction, thumb
points in F direction.
Ch 20
11
Magnetic Force on Current-Carrying Wire
Wire
I
l

F  I l B sin 
• l is the length of the wire inside of field
Ch 20
•F is into screen in above drawing
12
Example 20-2A. At a certain place the Earth’s magnetic field is 0.60 x 10-4 T,
pointing 75o below the horizontal in a north-south plane. A 10.0 m wire carries a
15-A current. If the current is directed horizontally toward the east, what is the
magnitude and direction of the magnetic force on the wire?
•The wire points out of the page.
•Force is perpendicular to current and B.
•Direction of force is shown. It is in the
plane formed by the north-south with the
vertical.
F  I l B sin 
F  (15 A)(10 m)(0.6  104 T)(sin 90 )
F  9  103 N
Ch 20
13
Example 20-2B. At a certain place the Earth’s magnetic field is 0.60 x 10-4 T,
pointing 75o below the horizontal in a north-south plane. A 10.0 m wire carries a
15-A current. What would be the magnitude and direction of the force if the
current is directed upward?
Direction of Force: into
paper or West
  165
F  I l B sin 
F  (15 A)(10 m)(0.6  104 T)(sin 165 )
3
F  2.3  10 N
Ch 20
14
Magnetic Force on Moving Charge
•Just as there is a force on a wire carrying a current,
there is also a force on a moving charge in a magnetic
field.
•Can again use right hand rule for a positive particle
moving with velocity v in magnetic field B
F  q v B sin 
Ch 20
15
Circular Path
•A charged particle moving perpendicular to a magnetic field
experiences a force perpendicular to velocity (centripetal force) resulting
in circular motion
magnetic force = centripetal force
m v2
qvB
r
r
mv
qB
•In figure, “x” indicates
B is into paper (like
feathers of an arrow)
and “•” indicates field
out of paper (like point
of arrow).
Ch 20
16
20-3. (61) In a mass spectrometer, germanium atoms have radii of curvature
equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an
atomic mass of 76 u. What are the atomic masses of the other isotopes?
All ions have the same velocity when they
enter magnetic field.
For circular motion:
mv
qvB
r
2
m qB

 constant
r
v
For r21 = 21.0 cm
m21.0
m
764
 
21.0 cm r 22.8 cm
Ch 20
m21.0
764

(21.0 cm)  70 u
22.8 cm
m21.6
764

(21.6 cm)  72 u
22.8 cm
m21.9
764

(21.9 cm)  73 u
22.8 cm
m22.2
764

(22.2 cm)  74 u
22.8 cm
17
Force Between Parallel Wires
•In the drawing below, the left wire produces a magnetic field.
Because of this field, the right wire experiences a force to the left.
•For the same reason, the left wire experiences force to right.
•If current I2 is reversed, the result
is the wires repel each other.
Ch 20
18
Torque on Current Loop
•A loop of wire carrying a current experiences a torque.
•This torque can cause it to rotate up to 1800
•If the current is then reversed, then it will rotate another 1800
•This is the basis for the electric motor.
Ch 20
•It is easy to reverse current mechanically and thus achieve
continuous rotation
19
Magnetic Field of Earth
•There is evidence that the earth’s magnetic field has reversed 5 or 6
times with a separation of about 200,000 years
•The next reversal is “overdue”
•The picture is the result of a computer model of the earths magnetic
field.
Ch 20
20
Magnetic Field of Earth
is Radiation Shield
protons
•The sun emits a stream of high speed protons
•The magnetic force on the protons bends them into the screen and
thus they don’t strike the earth
•This protects the earth from what would be a high radiation
environment.
•At times when the earths magnetic field is weak, evolutional changes
Ch 20
21
are accelerated.
Magnetic Field of Atoms
•An electron in an atomic orbit is similar to a loop of wire
carrying a current and thus produces a magnetic field.
•There is also a magnetic field from the “spin” of the
electron.
•The nucleus also has a magnetic field due to the motion of
the protons and neutrons and their spin.
•The above picture is simplistic because it does not consider
Ch 20
Quantum
Mechanics
22
Ferromagnetism
Iron atoms have a strong magnetic field and all of the atoms in a “domain”
of size ~ 1mm are oriented in the same direction. Thus each domain acts
like a strong magnet but the random orientation of the domains (see Fig A)
produces no net field. When placed in an external magnetic field, the
domains are preferentially aligned in one direction. In Fig. B the alignment
is downward. This results in a net field that is much stronger than the
original external field.
Ch 20
23