Copyright © 2009 Pearson Education, Inc. Chapter 30: Sources of the Magnetic Field.

Copyright © 2009 Pearson Education, Inc.

Chapter 30: Sources of the Magnetic Field


•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

Chapter Outline


Magnetic Field Due to a Long, Straight Current Carrying Wire: Direction

•Ch. 29: The magnetic fieldlines for a long, straight,current carrying wire arecircles concentric with the wire.•The field lines are in planesperpendicular to the wire.•The magnitude of the field isconstant on a circle of radius a.•Use the right-hand rule todetermine the direction of thefield, as shown.


Magnetic Field Due to a Current Carrying Wire

•A compass can be used todetect the magnetic field.•When there is no currentin the wire, there is nofield due to the current.•In this case, the compassneedles all point towardthe Earth’s north pole.•Due to the Earth’smagnetic field


•When the wire carries acurrent, the compassneedles deflect in adirection tangent to thecircle.•This shows the direction

ofthe magnetic fieldproduced by the wire.•If the current is reversed,the direction of the needlesalso reverses.

Magnetic Field Due to a Current Carrying Wire


The circular magnetic field around the wire is shown by the iron filings.


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:

Magnetic Field Due to a Straight 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!


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.

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

Calculation of B Near a Wire


ExampleMagnetic 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

ExampleMagnetic 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.


Conceptual ExampleMagnetic 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 b

Solution:

S:S: Solution:


Conceptual ExampleMagnetic 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 b


•The force F this field exertson a length ℓ2 of wire 2 is

Magnetic Force Between Two Parallel Wires•Recall from Ch. 29 that theforce F on a wire carrying currentI in a magnetic field B is:

•We’ve just seen that the magnetic

field B produced at the position ofwire 2 due to the current in wire 1 is:

The magnetic force between 2 currents is analogous to

the Coulomb electric force between 2 charges!!


Using the cross product form of the force:

& applying the right hand rule shows that

Parallel Currents ATTRACT

and

Anti-Parallel Currents REPEL.


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.


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


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.


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. Chapter 30: Sources of the Magnetic Field.

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