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Chapter 30: Sources of the Magnetic Field
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Chapter Outline
• Magnetic Field Due to a Straight Wire
• Force between Two Parallel Wires
• Definitions of the Ampere & the Coulomb
• Ampère’s Law
• Magnetic Field of a Solenoid and a Toroid
• Biot-Savart Law
• Magnetic Materials – Ferromagnetism
• Electromagnets and Solenoids – Applications
• Magnetic Fields in Magnetic Materials; Hysteresis
• Paramagnetism and Diamagnetism
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Magnetic Field Due to a Long, Straight
Current Carrying Wire: Direction
• Ch. 29: The magnetic field
lines for a long, straight,
current carrying wire are
circles concentric with the wire.
• The field lines are in planes
perpendicular to the wire.
• The magnitude of the field is
constant on a circle of radius a.
• Use the right-hand rule to
determine the direction of the
field, as shown.
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Magnetic Field Due to a Current Carrying Wire
• A compass can be used to
detect the magnetic field.
• When there is no current
in the wire, there is no
field due to the current.
• In this case, the compass
needles all point toward
the Earth’s north pole.
• Due to the Earth’s
magnetic field
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Magnetic Field Due to a Current Carrying Wire
• When the wire carries a
current, the compass
needles deflect in a
direction tangent to the
circle.
• This shows the direction of
the magnetic field
produced by the wire.
• If the current is reversed,
the direction of the needles
also reverses.
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The circular
magnetic field
around the wire is
shown by the iron
filings.
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Magnetic Field Due to a Straight Wire
Experimental Results show that the
Magnetic field B due to a straight,
current carying wire is proportional
to the Current I & inversely
proportional to the distance r from
the wire:
μ0 is a constant, called the permeability
of free space. It’s value is
μ0 = 4π  10-7 T·m/A.
It plays a similar role for magnetic
fields that ε0 plays for electric fields!
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Calculation of B Near a Wire
An electric wire in the wall of a
building carries a dc current
I = 25 A vertically upward.
Calculate the magnetic field B
due to this current at a point
P = 10 cm in the radial direction
from the wire.
Copyright © 2009 Pearson Education, Inc.
Calculation of B Near a Wire
An electric wire in the wall of a
building carries a dc current
I = 25 A vertically upward.
Calculate the magnetic field B
due to this current at a point
P = 10 cm in the radial direction
from the wire.
Solution
Use
This gives B = 5.0  10-5 T
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Example
Magnetic field midway between two currents.
Two parallel straight wires a distance 10.0 cm apart carry
currents in opposite directions. Current I1 = 5.0 A is out of the
page, and I2 = 7.0 A is into the page. Calculate the magnitude
& direction of the magnetic field halfway between the 2 wires.
Copyright © 2009 Pearson Education, Inc.
Example
Magnetic field midway between two currents.
Two parallel straight wires a distance 10.0 cm apart carry
currents in opposite directions. Current I1 = 5.0 A is out of the
page, and I2 = 7.0 A is into the page. Calculate the magnitude
& direction of the magnetic field halfway between the 2 wires.
Solution:
Use
for each wire. Then
add them as vectors
B = B1 + B2
B = 4.8  10-5 T
Copyright © 2009 Pearson Education, Inc.
Conceptual Example
Magnetic Field Due to 4 Wires
The figure shows 4 long parallel wires which carry equal
currents into or out of the page. In which configuration,
(a) or (b), is the magnetic field greater at the center of the square?
a
Solution:
S:
S:
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b
Solution:
Conceptual Example
Magnetic Field Due to 4 Wires
The figure shows 4 long parallel wires which carry equal
currents into or out of the page. In which configuration,
(a) or (b), is the magnetic field greater at the center of the square?
a
Copyright © 2009 Pearson Education, Inc.
b
Magnetic Force Between Two Parallel Wires
• Recall from Ch. 29 that the
force F on a wire carrying current
I in a magnetic field B is:
• We’ve just seen that the magnetic
field B produced at the position of
wire 2 due to the current in wire 1 is:
• The force F this field exerts
The magnetic force between
on a length ℓ2 of wire 2 is
2 currents is analogous to
the Coulomb electric force
between 2 charges!!
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Using the cross product
form of the force:
& applying the right hand
rule shows that
Parallel Currents
ATTRACT
and
Anti-Parallel
Currents REPEL.
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Example
Force Between Two
Current-carrying Wires.
The two wires of a 2.0-m
long appliance cord are
d = 3.0 mm apart & carry a
current I = 8.0 A dc.
Calculate the force one
wire exerts on the other.
Copyright © 2009 Pearson Education, Inc.
Example
Force Between Two
Current-carrying Wires.
The two wires of a 2.0-m
long appliance cord are
d = 3.0 mm apart & carry a
current I = 8.0 A dc.
Calculate the force one
wire exerts on the other.
Use:
Resulting in
F = 8.5  10-3 N
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Example
Suspending a wire with a current.
A horizontal wire carries a current I1 = 80 A dc. Calculate the
current I2 that a second parallel wire d = 20 cm below it must
carry so that it doesn’t fall due to gravity. The lower wire has a
mass per meter of (m/ℓ) = 0.12 g/m.
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Definitions of the Ampere & the Coulomb
The SI unit of current, the Ampere is officially defined in
terms of the force between two current-carrying wires:
One Ampere IS DEFINED as that current flowing
in each of two long parallel wires 1 m apart,
which results in a force of exactly F =2  10-7 N
per meter of length of each wire.
One Coulomb is IS DEFINED
as exactly 1 ampere-second.
Copyright © 2009 Pearson Education, Inc.