General Physics (PHYS )
Chapter 22
Magnetism
Magnetic Force Exerted on a
current
Magnetic Torque
Electric Currents, magnetic Fields,
and Ampere’s Law
Current Loops and Solenoids
Magnetism in Matter
GOT IT 4
1. To the left
2. To the right
0%
0%
Figure shows a flexible wire passing through a
magnetic field that points out of page.
The wire is deflected upward, as shown.
Is the current flowing
GOT IT 5 Power Line
1. Upward
2. Downward
3. Right
4. Left
0%
0%
0%
0%
A power line runs along Earth’s equator, where B points
horizontally from south to north; the line carries current flowing
from west to east.
What’s the direction of the magnetic force on the power line?
I F L B
Example 3: Making the Connection
Earth’s equatorial field strength is 30 T,
and the power line carries 500 A.
What’s the magnetic force on a kilometer
of the line.
I F L B
Loops of Current and Magnetic Torque
In the current loop shown, the vertical sides
experience forces that are equal in magnitude
and opposite in direction.
They do not operate at
the same point, so they
create a torque around
the vertical axis of the
loop.
Loops of Current and Magnetic Torque
The total torque is the sum of the torques from
each force:
Or, since A = hw,
Loops of Current and Magnetic Torque
To increase the torque, a long wire may be
wrapped in a loop many times, or “turns.” If the
number of turns is N, we have
Loops of Current and Magnetic Torque
The torque on a current loop is proportional to
the current in it, which forms the basis of a
variety of useful electrical instruments. Here is a
galvanometer:
Example 4: Hybrid Car Motor Toyota’s Prius gas-electric hybrid car uses a 50-kW electric
motor that develops a maximum torque of 400 Nm.
Suppose you want to produce this same torque in the
motor just discussed, with a 950-turn rectangular coil of
wire measuring 30 cm by 20 cm, in a uniform field of 50 mT.
How much current does the motor need?
Max torque at sin = 1 :
950-turn
coil
12
GOT IT : A rectangular loop is placed in a
uniform magnetic field with the plane of the
loop parallel to the direction of the field. If a
current is made to flow through the loop in
the sense shown by the arrows, the field
exerts on the loop:
1. a net force.
2. a net torque.
3. a net force and a net torque.
4. neither a net force nor a net torque.
Electric Currents, Magnetic Fields, and
Ampère’s Law
Experimental observation:
Electric currents can
create magnetic fields.
These fields form circles
around the current.
Electric Currents, Magnetic Fields, and
Ampère’s Law
To find the direction of the
magnetic field due to a
current-carrying wire, point
the thumb of your right
hand along the wire in the
direction of the current I.
Your fingers are now
curling around the wire in
the direction of the
magnetic field.
Electric Currents, Magnetic Fields, and
Ampère’s Law
The magnetic field is inversely proportional to
the distance from the wire:
Electric Currents, Magnetic Fields, and
Ampère’s Law
Ampère’s Law relates the current through a
surface defined by a closed path to the magnetic
field along the path:
Example 5
Problem 46. A long, straight wire carries a
current of 7.2 A. How far from this wire is
the magnetic field it produces equal to the
Earth’s magnetic field, which is
approximately 5.0 X 10-5 T?
Example 6
Problem 52. In Oersted’s experiment,
suppose that the compass was 0.25 m from
the current-carrying wire. If a magnetic field
of half the Earth’s magnetic field of 5.0 X 10-
5 T was required to give a noticeable
deflection of the compass needle, what
current must the wire have carried?
Electric Currents, Magnetic Fields, and
Ampère’s Law
Since a current-carrying wire experiences a force
in a magnetic field, and a magnetic field is created
by a current-carrying wire, there is a force
between current-carrying wires. Let’s study this
phenomenon
Electric Currents, Magnetic Fields, and
Ampère’s Law
Since a current-carrying wire experiences a force
in a magnetic field, and a magnetic field is created
by a current-carrying wire, there is a force
between current-carrying wires:
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Magnetic Field of a current loop
• Magnetic field produced by a wire can be enhanced by having the wire in a loop.
Dx1
I
Dx2
B
Current Loops
The magnetic field of a current loop is similar to
the magnetic field of a bar magnet.
In the center of the loop,
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Solenoid
• Solenoid magnet consists of a wire coil with multiple loops.
• It is often called an electromagnet.
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Solenoid Magnet
• Field lines inside a solenoid magnet are parallel, uniformly spaced and close together.
• The field inside is uniform and strong.
• The field outside is non uniform and much weaker.
• One end of the solenoid acts as a north pole, the other as a south pole.
• For a long and tightly looped solenoid, the field inside has a value:
Solenoids
Solenoid: a long, tightly wounded coil.
0B n I
Boutside = 0
Application: magnetic switches, valves, ….
N turns per unit
length.
.
Example 7 MRI Scanner The solenoid used in an MRI scanner is 2.4 m long & 95 cm in diameter.
It’s wounded from superconducting wire 2.0 mm in diameter,
with adjacent turns separated by an insulating layer of negligible
thickness.
Find the current that will produce a 1.5-T magnetic field inside the
solenoid. wire diameter = 1/500 m
n = 500 turns/m
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Example 8: Magnetic Field inside a Solenoid.
Consider a sole noid consisting of 100 turns of wire and length of 10.0 cm. Find the magnetic field inside when it carries a current of 0.500 A.
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Comparison: Electric Field vs. Magnetic Field
Electric Magnetic
Source Charges Moving Charges
Acts on Charges Moving Charges
Force F = Eq F = q v B sin()
Direction Parallel E Perpendicular to v,B
Field Lines
Opposites Charges Attract Currents Repel
http://www.youtube.com/watch?v=
QGytW_C6hR8
MAGNETS…MAGNETS
Magnetism in Matter
The electrons surrounding an atom create
magnetic fields through their motion. Usually
these fields are in random directions and have
no net effect, but in some atoms there is a net
magnetic field.
If the atoms have a strong tendency to align
with each other, creating a net magnetic field,
the material is called ferromagnetic.
Magnetism in Matter
Ferromagnets are characterized by domains,
which each have a strong magnetic field, but
which are randomly oriented. In the presence of
an external magnetic field, the domains align,
creating a magnetic field within the material.
Magnetism in Matter
Permanent magnets
are ferromagnetic;
such materials can
preserve a “memory”
of magnetic fields that
are present when the
material cools or is
formed.
Magnetism in Matter
Many materials that are not ferromagnetic are
paramagnetic – they will partially align in a
strong magnetic field, but the alignment
disappears when the external field is gone.
Finally, all materials exhibit diamagnetism – an
applied magnetic field induces a small
magnetic field in the opposite direction in the
material.
Magnetism in Matter
Summary of Chapter 22
• All magnets have two poles, north and south.
• Magnetic fields can be visualized using
magnetic field lines. These lines point away
from north poles and toward south poles.
• The Earth produces its own magnetic field.
• A magnetic field exerts a force on an electric
charge only if it is moving:
• A right-hand rule gives the direction of the
magnetic force on a positive charge.
Summary of Chapter 22
• If a charged particle is moving parallel to a
magnetic field, it experiences no magnetic force.
• If a charged particle is moving perpendicular to a
magnetic field, it moves in a circle:
• If a charged particle is moving at an angle to a
magnetic field, it moves in a helix.
Summary of Chapter 22
• A wire carrying an electric current also may
experience a force in a magnetic field; the force
on a length L of the wire is:
• A current loop in a magnetic field may
experience a torque:
Summary of Chapter 22
• Electric currents create magnetic fields; the
direction can be determined using a right-hand
rule.
• Ampère’s law:
• Magnetic field of a long, straight wire:
• Force between current-carrying wires:
Summary of Chapter 22
• The magnetic field of a current loop is similar to
that of a bar magnet.
• The field in the center of the loop is:
• Magnetic field of a solenoid:
Summary of Chapter 22
• A paramagnetic material has no magnetic field,
but will develop a small magnetic field in the
direction of an applied field.
• A ferromagnetic material may have a permanent
magnetic field; when placed in an applied field it
develops permanent magnetization.
• All materials have a small diamagnetic effect;
when placed in an external magnetic field they
develop a small magnetic field opposite to the
applied field.