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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

If the plane of the loop is at an angle to the

magnetic field,

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:

Application: Electric Motors

Rotating loop

Brushes

Commutator

Battery

CCW

CW

Always CCW

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:

Ampère’s Law

WARNING!!

B and L need to be parallel

Ampère’s Law

We can use Ampère’s Law to find the magnetic

field around a long, straight wire:

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?

FROM BOOK: Active Example 22-2

I hope you worked on this example.

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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What can we do to create a stronger magnet?

Well, we add more

turns/loops

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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:

Current Loops and Solenoids

We can use Ampère’s Law to find the field inside

the solenoid:

Solenoids

Solenoid: a long, tightly wounded coil.

0B n I

Boutside = 0

Application: magnetic switches, valves, ….

N turns per unit

length.

.

Field of a solenoid is very similar to that of a bar magnet.

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.