Copyright © 2009 Pearson Education, Inc. Chapter 27 Magnetism.

Copyright © 2009 Pearson Education, Inc.

Chapter 27Magnetism


The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation:

This equation defines the magnetic field B.

In vector notation:

27-3 Force on an Electric Current in a Magnetic Field; Definition of BB

��

B��


Unit of B: the tesla, T:

1 T = 1 N/A·m.

Another unit sometimes used: the gauss (G):

1 G = 10-4 T.

27-3 Force on an Electric Current in a Magnetic Field; Definition of BB

��


27-3 Force on an Electric Current in a Magnetic Field; Definition of B

Example 27-1: Magnetic Force on a current-carrying wire.

A wire carrying a 30-A current has a length l = 12 cm between the pole faces of a magnet at an angle θ = 60°, as shown. The magnetic field is approximately uniform at 0.90 T. We ignore the field beyond the pole pieces. What is the magnitude of the force on the wire?

B��


27-3 Force on an Electric Current in a Magnetic Field; Definition of B

Example 27-3: Magnetic Force on a semicircular wire.

A rigid wire, carrying a current I, consists of a semicircle of radius R and two straight portions as shown. The wire lies in a plane perpendicular to a uniform magnetic field B0. Note choice of x and y axis. The straight portions each have length l within the field. Determine the net force on the wire due to the magnetic field B0.

B��

B��

B��


The force on a moving charge is related to the force on a current since a current is just a bunch of moving charges:

Once again, the direction is given by a right-hand rule.

27-4 Force on an Electric Charge Moving in a Magnetic Field



Conceptual Example 27-4: Negative charge near a magnet.

A negative charge -Q is placed at rest near a magnet. Will the charge begin to move? Will it feel a force? What if the charge were positive, +Q?



Example 27-5: Magnetic force on a proton.

A magnetic field exerts a force of 8.0 x 10-14 N toward the west on a proton moving vertically upward at a speed of 5.0 x 106 m/s (a). When moving horizontally in a northerly direction, the force on the proton is zero (b). Determine the magnitude and direction of the magnetic field in this region. (The charge on a proton is q = +e = 1.6 x 10-19 C.)


If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.




Example 27-7: Electron’s path in a uniform magnetic field.

An electron travels at 2.0 x 107 m/s in a plane perpendicular to a uniform 0.010-T magnetic field. Describe its path quantitatively.


Problem solving: Magnetic fields – things to remember:

1.The magnetic force is perpendicular to the magnetic field direction.

2.The right-hand rule is useful for determining directions.

3.Equations in this chapter give magnitudes only. The right-hand rule gives the direction.


1) out of the page1) out of the page

2) into the page2) into the page

3) zero3) zero

4) to the right4) to the right

5) to the left5) to the left

vv

qq

ConcepTest 27.1c ConcepTest 27.1c Magnetic Force IIIMagnetic Force III

A positive charge enters a A positive charge enters a

uniform magnetic field as uniform magnetic field as

shown. What is the direction shown. What is the direction

of the magnetic force?of the magnetic force?

Using the right-hand rule, you can

see that the magnetic force is

directed into the pageinto the page. Remember

that the magnetic force must be

perpendicularperpendicular to to BOTHBOTH the the BB field field

and the velocityand the velocity.

1) out of the page1) out of the page

2) into the page2) into the page

3) zero3) zero

4) to the right4) to the right

5) to the left5) to the left

vv

qqFF

ConcepTest 27.1c ConcepTest 27.1c Magnetic Force IIIMagnetic Force III

A positive charge enters a A positive charge enters a

uniform magnetic field as uniform magnetic field as

shown. What is the direction shown. What is the direction

of the magnetic force?of the magnetic force?

ConcepTest 27.3 ConcepTest 27.3 Magnetic FieldMagnetic Field

xx

yy

A proton beam enters a A proton beam enters a

magnetic field region as shown magnetic field region as shown

below. What is the direction of below. What is the direction of

the magnetic field the magnetic field BB? ?

1) + 1) + yy

2) 2) –– yy

3) +3) + x x

4) + 4) + zz (out of page) (out of page)

5) 5) –– zz (into page) (into page)

The picture shows the force acting

in the ++yy direction direction. Applying the

right-hand rule leads to a B field

that points into the pageinto the page. The B

field must be out of the planeout of the plane

because B B v v and B B F F.

ConcepTest 27.3 ConcepTest 27.3 Magnetic FieldMagnetic Field

xx

yy

A proton beam enters a A proton beam enters a

magnetic field region as shown magnetic field region as shown

below. What is the direction of below. What is the direction of

the magnetic field the magnetic field BB? ?

1) + 1) + yy

2) 2) –– yy

3) + 3) + xx

4) + 4) + zz (out of page) (out of page)

5) 5) –– zz (into page) (into page)

Follow-up:Follow-up: What would happen to a beam of atoms? What would happen to a beam of atoms?



Conceptual Example 27-9: A helical path.

What is the path of a charged particle in a uniform magnetic field if its velocity is not perpendicular to the magnetic field?



The aurora borealis (northern lights) is caused by charged particles from the solar wind spiraling along the Earth’s magnetic field, and colliding with air molecules.


The forces on opposite sides of a current loop will be equal and opposite (if the field is uniform and the loop is symmetric), but there may be a torque.

The magnitude of the torque is given by

27-5 Torque on a Current Loop; Magnetic Dipole Moment


The quantity NIA is called the magnetic dipole moment, μ:


The potential energy of the loop depends on its orientation in the field:



Example 27-12: Magnetic moment of a hydrogen atom.

Determine the magnetic dipole moment of the electron orbiting the proton of a hydrogen atom at a given instant, assuming (in the Bohr model) it is in its ground state with a circular orbit of radius r = 0.529 x 10-10 m. [This is a very rough picture of atomic structure, but nonetheless gives an accurate result.]



Example: A rectangular coil 5.40 cm X 8.50 cm consists of 25 turns of wire and carries a current of 15.0 mA. A 0.350-T magnetic field is applied parallel to the plane of the coil.a)Calculate the magnitude of the magnetic dipole moment of the coil.b)What is the magnitude of the torque acting on the loop?



a)

b)

3

3 2

25 15.0 10 0.054 0.085

1.72 10

coil NIA A m m

A m

3 2

4

Note: sin90

1.72 10 0.350

6.02 10

ocoil coil coil coilB B B B

A m T

N m


27-6 Applications: Motors

An electric motor uses the torque on a current loop in a magnetic field to turn magnetic energy into kinetic energy.


A galvanometer takes advantage of the torque on a current loop to measure current; the spring constant is calibrated so the scale reads in amperes.

27-6 Applications: Galvanometers

If there is a current in If there is a current in

the loop in the direction the loop in the direction

shown, the loop will:shown, the loop will:

1) move up1) move up

2) move down2) move down

3) rotate clockwise3) rotate clockwise

4) rotate counterclockwise4) rotate counterclockwise

5) both rotate and move5) both rotate and move

N S

NS

BB field out of North field out of NorthBB field into South field into South

ConcepTest 27.7b ConcepTest 27.7b Magnetic Force on a Loop IIMagnetic Force on a Loop II

Look at the north pole: here the

magnetic field points to the rightright and

the current points out of the pageout of the page.

The right-hand rule says that the force

must point upup. At the south pole, the

same logic leads to a downwarddownward force.

Thus the loop rotates clockwiseclockwise.

N S

F

F

1) move up1) move up

2) move down2) move down

3) rotate clockwise3) rotate clockwise

4) rotate counterclockwise4) rotate counterclockwise

5) both rotate and move5) both rotate and move

If there is a current in If there is a current in

the loop in the direction the loop in the direction

shown, the loop will:shown, the loop will:

ConcepTest 27.7b ConcepTest 27.7b Magnetic Force on a Loop IIMagnetic Force on a Loop II


27-7 Discovery and Properties of the Electron

Electrons were first observed in cathode ray tubes. These tubes had a very small amount of gas inside, and when a high voltage was applied to the cathode, some “cathode rays” appeared to travel from the cathode to the anode.



The value of e/m for the cathode rays was measured in 1897 using the apparatus below; it was then that the rays began to be called electrons.

Figure 27-30 goes here.



Millikan measured the electron charge directly shortly thereafter, using the oil-drop apparatus diagrammed below, and showed that the electron was a constituent of the atom (and not an atom itself, as its mass is far too small).

The currently accepted values of the electron mass and charge are

m = 9.1 x 10-31 kg

e = 1.6 x 10-19 C


27-8 The Hall EffectWhen a current-carrying wire is placed in a magnetic field, there is a sideways force on the electrons in the wire. This tends to push them to one side and results in a potential difference from one side of the wire to the other; this is called the Hall effect. The emf differs in sign depending on the sign of the charge carriers; this is how it was first determined that the charge carriers in ordinary conductors are negatively charged.


A mass spectrometer measures the masses of atoms. If a charged particle is moving through perpendicular electric and magnetic fields, there is a particular speed at which it will not be deflected, which then allows the measurement of its mass:

27-9 Mass Spectrometer


All the atoms reaching the second magnetic field will have the same speed; their radius of curvature will depend on their mass.




Example 27-14: Mass spectrometry.

Carbon atoms of atomic mass 12.0 u are found to be mixed with another, unknown, element. In a mass spectrometer with fixed B′, the carbon traverses a path of radius 22.4 cm and the unknown’s path has a 26.2-cm radius. What is the unknown element? Assume the ions of both elements have the same charge.


• Magnets have north and south poles.

• Like poles repel, unlike attract.

• Unit of magnetic field: tesla.

• Electric currents produce magnetic fields.

• A magnetic field exerts a force on an electric current:

Summary of Chapter 27


• A magnetic field exerts a force on a moving charge:

Summary of Chapter 27

• Torque on a current loop:

• Magnetic dipole moment:


Chapter 28Sources of Magnetic Field


The magnetic field due to a straight wire is inversely proportional to the distance from the wire:

The constant μ0 is called the permeability of free space, and has the value

μ0 = 4π x 10-7 T·m/A. (exactly!)

28-1 Magnetic Field Due to a Straight Wire



Example 28-1: Calculation of B near a wire.

An electric wire in the wall of a building carries a dc current of 25 A vertically upward. What is the magnetic field due to this current at a point P 10 cm due north of the wire?

B��



Example 28-2: Magnetic field midway between two currents.

Two parallel straight wires 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. Determine the magnitude and direction of the magnetic field halfway between the two wires.



Conceptual Example 28-3: Magnetic field due to four wires.

This figure shows four 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?

Each of the wires in the figures below carry the same current, either into or out of the page. In which case is the magnetic field at the center of the square greatest?

1) arrangement 11) arrangement 1



4) same for all4) same for all

1 2 3B = ? B = ?B = ?

ConcepTest 28.1b ConcepTest 28.1b Magnetic Field of a Wire IIMagnetic Field of a Wire II

1 2 3

ConcepTest 28.1b ConcepTest 28.1b Magnetic Field of a Wire IIMagnetic Field of a Wire II

Each of the wires in the figures below carry the same current, either into or out of the page. In which case is the magnetic field at the center of the square greatest?




4) same for all4) same for all


The magnetic field produced at the position of wire 2 due to the current in wire 1 is

The force this field exerts on a length l2 of wire 2 is

28-2 Force between Two Parallel Wires

0 1

2 2 2 1 2 2

0 1 22

2

2

IF I B I

d

I I

d


Parallel currents attract; antiparallel currents repel.

RIGHT HAND RULE!!




Example 28-5: Suspending a wire with a current.

A horizontal wire carries a current I1 = 80 A dc. A second parallel wire 20 cm below it must carry how much current I2 so that it doesn’t fall due to gravity? The lower wire has a mass of 0.12 g per meter of length.

Copyright © 2009 Pearson Education, Inc. Chapter 27 Magnetism.

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Transcript of Copyright © 2009 Pearson Education, Inc. Chapter 27 Magnetism.