Lecture PowerPoints Chapter 20 Physics: Principles with

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Lecture PowerPoints

Chapter 20 Physics: Principles with Applications, 7th edition

Giancoli

Chapter 20 Magnetism


Contents of Chapter 20

•  Magnets and Magnetic Fields

•  Electric Currents Produce Magnetic Fields

•  Force on an Electric Current in a Magnetic Field; Definition of B

•  Force on Electric Charge Moving in a Magnetic Field

•  Magnetic Field Due to a Long Straight Wire

•  Force between Two Parallel Wires


Contents of Chapter 20

•  Solenoids and Electromagnets

•  Ampère’s Law

•  Torque on a Current Loop; Magnetic Moment

•  Applications: Galvanometers, Motors, Loudspeakers

•  Mass Spectrometer

•  Ferromagnetism: Domains and Hysteresis


20-1 Magnets and Magnetic Fields

Magnets have two ends—poles—called north and south.

Like poles repel; unlike poles attract.



However, if you cut a magnet in half, you don’t get a north pole and a south pole—you get two smaller magnets.



Magnetic fields can be visualized using magnetic field lines, which are always closed loops.



The Earth’s magnetic field is similar to that of a bar magnet.

Note that the Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.



A uniform magnetic field is constant in magnitude and direction.

The field between these two wide poles is nearly uniform.


20-2 Electric Currents Produce Magnetic Fields

Experiment shows that an electric current produces a magnetic field.


20-2 Electric Currents Produce Magnetic Fields

The direction of the field is given by a right-hand rule.


20-3 Force on an Electric Current in a Magnetic Field; Definition of B

A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.


20-3 Force on an Electric Current in a Magnetic Field; Definition of B

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.


(20-1)

Unit of B: the tesla, T.

1 T = 1 N/A·m

Another unit sometimes used: the gauss (G).

1 G = 10−4 T

Example

The force on a wire is a maximum of 8.5×10-2 N when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic filed is vertical. The wire is observed to “jump” towards the observer when the current is turned on. (a) What type of magnetic pole is the top pole face? (b) If the pole faces have a diameter of 10 cm, estimate the current in the wire if the filed is 0.22 T. (c) If the wire is tipped so that it makes an angle of 10° with the horizontal, what force will it now feel?


20-4 Force on Electric Charge Moving in a Magnetic Field

The force on a moving charge is related to the force on a current:

The direction is given by a right-hand rule.


(20-3)

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


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.




Example

A helium ion (Q=+2e) whose mass is 6.6×10−27 kg is accelerated by a voltage of 3700 V. (a) What is its speed? (b) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.34 T field? ( c) What is its period of revolution?


20-5 Magnetic Field Due to a Long Straight Wire

The field 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


(20-6)

20-6 Force between Two Parallel Wires

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:


(20-7)

20-6 Force between Two Parallel Wires

Parallel currents attract; antiparallel currents repel.


Summary (1)

•  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 (2)

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

•  Magnitude of the field of a long, straight current-carrying wire:

•  Parallel currents attract; antiparallel currents repel


20-7 Solenoids and Electromagnets

A long coil of wire consisting of many loops or turns is called a solenoid. If it is tightly wrapped, the magnetic field in its interior is almost uniform: A solenoid acts like a magnet. One end can be considered as the north pole, and the other as south pole (depend on the direction of the current in the loops)


(20-8)


If a piece of iron is inserted in the solenoid, the magnetic field greatly increases, because the iron becomes a magnet. The resulting magnetic field is the sum of the field due to the current and the field due to the iron, and can be hundreds or thousands time of the field due to the current alone. Iron-core solenoid is an electromagnet.



Electromagnets have many practical applications: use in motors to producing large magnetic fields for research.

Doorbell: When the curcuit is closed by pushing the button, the coil becomes a magnet and exerts a force on the iron rod. The rod is pulled into the coil and strikes the bell.


20-8 Ampère’s Law We know the relation between the current in a long wire and the magnetic field – valid only for long wire.

Consider any (arbitrary) closed path around a current. Let us break this path in small segments Δl. We take the product of the length of this segment and component of the magnetic field parallel to this segment. Ampère’s law relates the magnetic field around a closed loop to the total current flowing through the loop.


(20-9)

20-8 Ampère’s Law

Ampère’s law can be used to calculate the magnetic field in situations with a high degree of symmetry.


The magnitude of the field at P: Choose the path of a circle with radius r, because at any point of this path the B is parallel to a segment on this path.

Because of symmetry, all Bi are the same.

€

B1Δl1 + B2Δl2 + ... + B100Δl100 = µ0I

€

B⋅ Δl1 + Δl2 + ... + Δl100( ) = µ0I

B⋅ 2πr = µ0I ⇒ B =µ0I2πr

20-8 Ampère’s Law

Ampère’s law can be used to calculate the magnetic field inside a solenoid. Let us choose a contour as shown by red line:

The first term = 0 because the field outside is negligible compared to the field inside the solenoid. Field B is perpendicular to the segments bc and da,so these terms = 0 too.


Then we can write: €

B||Δl( )ab + B||Δl( )bc + B||Δl( )cd + B||Δl( )da = µ0Ienc

€

B||Δl( )cd = µ0IencBℓ = µ0NI⇒

B =µ0NIℓ

20-9 Torque on a Current Loop; Magnetic Moment

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


(20-10)

(20-11)

Example 1

•  Use Ampere’s law to show that the magnetic field between the conductors of a coaxial cable is if r is greater than the radius of the inner wire and less than the radius of the outer wire. Show that B=0 outside the coaxial cable.


Example 2

•  A single square loop of wire 22 cm on a side is placed with its face to the magnetic field. When 5.7 A flows on the coil. the torque on it is 0.325 m�N. What is the magnetic field strength?


20-10 Applications: Galvanometers, Motors, Loudspeakers

A galvanometer takes advantage of the torque on a current loop to measure current.



An electric motor also takes advantage of the torque on a current loop, to change electrical energy to mechanical energy.



Loudspeakers use the principle that a magnet exerts a force on a current-carrying wire to convert electrical signals into mechanical vibrations, producing sound.


20-11 Mass Spectrometer

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:


20-11 Mass Spectrometer

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


20-12 Ferromagnetism: Domains and Hysteresis

Ferromagnetic materials are those that can become strongly magnetized, such as iron and nickel.

These materials are made up of tiny regions called domains; the magnetic field in each domain is in a single direction.



When the material is unmagnetized, the domains are randomly oriented. They can be partially or fully aligned by placing the material in an external magnetic field.



A magnet, if undisturbed, will tend to retain its magnetism. It can be demagnetized by shock or heat.

The relationship between the external magnetic field and the internal field in a ferromagnet is not simple, as the magnetization can vary.



Starting with unmagnetized material and no magnetic field, the magnetic field can be increased, decreased, reversed, and the cycle repeated. The resulting plot of the total magnetic field within the ferromagnet is called a hysteresis curve.


Summary of Chapter 20

•  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:



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

•  Magnitude of the field of a long, straight current-carrying wire:

•  Parallel currents attract; antiparallel currents repel



•  Magnetic field inside a solenoid:

•  Ampère’s law:

•  Torque on a current loop:


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Lecture PowerPoints Chapter 20 Physics: Principles with