Magnetism www.njctl.org Slide 3 / 162 Slide 4 / 162 Table of - - PDF document

Slide 1 / 162 Slide 2 / 162

www.njctl.org

Magnetism

Slide 3 / 162 How to Use this File

· Each topic is composed of brief direct instruction · There are formative assessment questions after every topic denoted by black text and a number in the upper left. · Students work in groups to solve these problems but use student responders to enter their own answers. · Designed for SMART Response PE student response systems. · Use only as many questions as necessary for a sufficient number of students to learn a topic. · Full information on how to teach with NJCTL courses can be found at njctl.org/courses/teaching methods

Slide 4 / 162 Table of Contents

· The Nature of Magnetism · Magnetic Fields · Origin and direction of Magnetic Fields · Magnetic Field force on a moving Electric Charge · Magnetic Field force on a current carrying wire · Magnetic Field due to a long, straight current carrying wire · Magnetic Field force between two current carrying wires · Mass Spectrometer

Click on the topic to go to that section

· Summary

Slide 5 / 162

The Nature of Magnetism

Return to Table

• f Contents

Slide 6 / 162 History

Magnets were first discovered over 2000 years ago by the Chinese and the Greeks and were used for various non scientific purposes. The name was coined by the Greeks, as certain magnetic rocks (magnetite) were found in the province of Magnesia. Unlike electrical effects due to the rubbing of various substances, like amber, to separate the electrical charges so there would be attractive and repulsive forces, these magnets came out of the ground already attracting and repelling certain materials.

Slide 7 / 162 History

It wasn't until after the 1000 A.D. that Chinese, European and Persian mariners separately used magnets for navigation. When a magnetic material, shaped in the form of a needle and floated on the surface of water, it always pointed in the same direction - towards the north. Always being able to tell which direction was north was a critical factor in ushering in the age of exploration. It wasn't until 1600 when this phenomenon was explained by William Gilbert. But first, the nature of magnetism will be discussed.

Slide 8 / 162 Magnet Properties

Magnets have two ends (poles) called north and south. Like poles repel; unlike poles attract. This attraction or repulsion is the magnetic force. These are examples of bar magnets.

Slide 9 / 162 Magnetic Poles

When a magnet is cut in half, each piece still has a north and a south

• pole. No matter how many times the magnet is cut, the pieces still

have a north and south pole. This works all the way down to the atomic level!

Slide 10 / 162 Magnetic Poles and Electric charges

The behavior of magnetic poles (north and south) are similar to electric charges (positive and negative) where opposite poles/ charges attract and like poles/charges repel. There are two significant differences between these effects. One, certain materials are naturally magnetic, where electrical properties result from physical rubbing. And secondly - there are independent positive and negative charges, but magnetic materials always contain a north and a south pole.

Slide 11 / 162

1 What are the two kinds of magnetic poles?

A North and Negative. B South and Positive. C Postive and Negative. D North and South.

Slide 12 / 162

2 Which of the following combination of magnetic poles will exert an attractive force on each other?

A North and North. B North and South. C South and South.

Slide 13 / 162

3 It is possible to find a magnet that only has a north pole? Yes No

Slide 14 / 162

4 Explain the similarities and the differences between electric charges and magnetic poles.

Students type their answers here

Slide 15 / 162

Magnetic Fields

Return to Table

• f Contents

Slide 16 / 162 Magnetic Fields

What's nice about Magnetic field lines is that they are more easily "seen." The above is a picture of iron filings sprinkled on a paper

• n top of a bar magnet.

Electric field lines were used to show how electric charges would exert forces on other charges. A similar concept will be used in Magnetism.

Slide 17 / 162 Magnetic Fields

The field exits one end of the magnet and returns to the other

• end. Note also, that the field lines extend through the magnet,

making a complete loop (unlike Electric Field Lines). The iron filings act like little bar magnets, and align with the magnetic field of the large magnet.

The red line shows a complete magnetic field line loop. The blue line shows a magnetic field line going through the magnet, and completing the loop outside of the picture.

Slide 18 / 162 Magnetic Fields

Arbitrarily, magnetic field lines are defined as leaving the north pole of the magnet and reentering at the south pole as seen below. The lines specify the direction that the north pole of a magnet will point to. The more lines per unit area, the stronger the field.

N

S

The lines that seem not to be in loops are - we just ran out

• f room on the slide. All

magnetic field lines form complete loops. The field lines also go right through the magnet, but are left out of the picture so you can see the pole labels.

Slide 19 / 162 Magnetic Fields

Like Electric Fields, different configurations of magnets will produce interesting Magnetic Fields. Here are two magnets with their north poles next to each other - these magnets are repelling each other.

Slide 20 / 162 Magnetic Fields

Like Electric Fields, different configurations of magnets will produce interesting Magnetic Fields. Here are two magnets with their opposite poles next to each other

• these magnets are attracting each other.

Slide 21 / 162

5 Magnetic field lines are drawn to represent the direction

• f the magnetic field at points in space. What convention

is used for the directions? Select two answers. A Magnetic field lines originate on a south pole. B Magnetic field lines originate on a north pole. C Magnetic field lines terminate on a south pole. D Magnetic field lines terminate on a north pole.

Slide 22 / 162

6 Magnetic field lines: A start on a north pole and extend to infinity. B start on a north pole and extend to infinity. C start on a south pole, loop around and return to a north pole. D start on a north pole, loop around and return to a south pole.

Slide 23 / 162 The Earth's Magnetic Field

The Earth’s magnetic field is similar to that of a bar magnet. It is caused by the circulation of molten iron alloys in the earth's outer core (more on this later). The Earth’s “North Pole” is really a south magnetic pole as the north ends of magnets are attracted to it. The magnetic poles are not located along the earth's axis of rotation.

Slide 24 / 162 The Earth's Magnetic Field

The Magnetic Field extends from the core to the outer limits of the atmosphere (magnetosphere). This picture (not to scale) shows the interaction of the solar wind (ions and electrons) with the earth's magnetic field that produces the magnetosphere.

Slide 25 / 162 The Earth's Magnetic Field

The Magnetic Field protects life on earth from being subjected to ionizing radiation that would cause great harm. The ions coming from the sun are deflected by the earth's magnetic field at the poles (where it's the strongest), and as they spiral down, they give off much of their energy as light.

Slide 26 / 162 The Earth's Magnetic Field

This kinetic energy to light energy transformation produces the Aurora Borealis and Aurora Australis.

Slide 27 / 162

7 The earth's magnetic north pole is located at: A the North geographic pole. B the South geographic pole. C in Alaska. D in Australia.

Slide 28 / 162

8 Why are the Aurora Borealis and the Aurora Australis produced over the south and north magnetic poles? A Because of the earth's angle of inclination in its

• rbit about the sun.

B The earth is slightly flattened at both poles. C The earth's magnetic field is weakest at the poles. D The earth's magnetic field is strongest at the poles.

Slide 29 / 162 Magnetic Field Units

The symbol for the Magnetic Field is B. The field is a vector and has both magnitude and direction. The unit of B is the Tesla, T, where Because the Tesla is such a large magnitude, another unit is frequently used, the Gauss, G, where To gain perspective, the magnetic field of the Earth at its surface is around 0.5 x 10-4 T or simply 0.5 G.

Slide 30 / 162 Magnetic Field Units

Carl Friedrich Gauss 1777-1855 - Mathematician and Physicist. Nikola Tesla 1856-1943, Inventor, Engineer, Physicist.

Slide 31 / 162

Origin and direction of Magnetic Fields

Return to Table

• f Contents

Slide 32 / 162 Electric Currents Produce Magnetic Fields

In 1819, while searching for a relationship between electricity and magnetism, Hans Christian Oersted set up a current carrying wire above a magnetized needle as seen in the drawing below from a text by Agustin Privat-Deschanel (1876)

http://books.google.com/books?id=lroQAQAAMAAJ&pg=PA656

Click here to see what a 19th century Physics textbook looks like!

Slide 33 / 162 Electric Currents Produce Magnetic Fields

When there was no current in the wire, the needle aligned with the magnetic field of the earth and pointed north. When current was supplied, the magnetized needle rotated on the pivot and pointed at a right angle to the electric wire. The direction of this rotation would depend on the direction of the current.

http://books.google.com/books?id=lroQAQAAMAAJ&pg=PA656

Slide 34 / 162 Electric Currents Produce Magnetic Fields

Oersted deduced that an electric current produced a magnetic field that affected the compass needle more strongly than the earth's magnetic field. In addition to this first experimental evidence that electric and magnetic fields are related, Oersted produced Aluminum for the first time from a chemical reaction of aluminum chloride. Aluminum was used in the 1960's for household wiring in the USA because it was cheaper than copper. It was later banned for household wiring as it would oxidize at connection points, increasing its resistance, and it would heat up, sometimes melting and causing fires.

Slide 35 / 162 Electric Currents Produce Magnetic Fields

Hans Christian Oersted (1777-1851) Physicist and Chemist Current carrying wire generating a magnetic field that deflects a compass needle.

Slide 36 / 162 The Earth's Magnetic Field

Remember this slide from earlier? It stated that the Earth's magnetic field is caused by the circulation of molten alloys in the earth's

• uter core.

Picture the molten alloys as having many, many free electrons that move together

• and you have a current.

Which is what Oersted demonstrated - currents create magnetic fields.

Slide 37 / 162

9 Hans Christian Oersted observed which of the following? A A magnetic field generates a current. B A current generates a magnetic field. C A changing magnetic field generates a current. D A current has no effect on a magnetic compass.

Slide 38 / 162

10 What is the geometric shape of the magnetic field surrounding a current carrying wire? A Circle. B Triangle. C Straight Line pointing away from the wire. D Straight Line pointing towards the wire.

Slide 39 / 162

11 The earth's magnetic field is generated by: A the movement of large quantities of molten metals in the outer core. B large deposits of magnetic ore in the earth's crust. C a solid mass of solid magnetic material in the core. D the interaction of the earth's core with radiation from the sun.

Slide 40 / 162

Oersted observed that the direction of the magnetic field depends

• n the direction of the electric current.

The direction of the field is given by the right-hand rule (actually through the use of vector calculus, but the right-hand rule gives the correct result). Orient your right hand thumb in the direction of the current. The B field follows the path followed by your curled fingers.

Electric Currents Produce Magnetic Fields Slide 41 / 162

To find the magnetic field at any point on the concentric circles, you draw a tangent to the circle. The tangent line points in the direction of the magnetic field at that point. There is no component of the magnetic field pointing towards the wire.

Electric Currents Produce Magnetic Fields Slide 42 / 162

When you have a current circulating around an iron core, a magnetic field is created and the device is called an electromagnet. This is an industrial electromagnet that when the current is turned on, it picks up metallic objects. Metal scrap is being attracted from the ground to the electromagnet.

Electric Currents Produce Magnetic Fields

Slide 43 / 162

12 A large iron disc is surrounded by many loops of a current carrying wire. When there is no current present, the iron is not magnetized - it cannot attract metal. The current is turned on and it attracts metal. What happens when the current is turned off? What would be a physical application of this?

Students type their answers here

Slide 44 / 162

13 To find the direction of the magnetic field about a current carrying wire, you point the thumb of your _______hand _______the direction of the current flow in the wire. You curl your fingers about the wire and that shows the direction of the magnetic field. A right, opposite B right, in C left, opposite D left, in

Slide 45 / 162

Another difference between electric fields and magnetic fields, is that we can normally understand an electric field very on two dimensional paper (the electric field is, of course, three dimensional, but is easily represented in two dimensions). But, as you just saw with Oersted's experiment, the magnetic field is looping around the wire so magnetic fields need to be shown as three dimensional to be understood. Somehow, we need to show this third dimension on our paper. We have left / right: Up / down: How do we represent the third dimension on a page of paper?

Electric Currents Produce Magnetic Fields Slide 46 / 162 Vector Symbols

Picture the field line (which is a vector with magnitude and direction) like an arrow. The head of the arrow is the direction of the field. If the magnetic field is into the page, you will see the tail of the arrow: If the magnetic field is out of the page, you will see the front of the arrow:

Slide 47 / 162

Here's how the magnetic field would look inside a current carrying loop. Your thumb points in the direction of the current, and your fingers curl around and show the magnetic field coming

• ut of the board within the loop.

What direction is the magnetic field outside the loop? That's right - into the board, as your fingers continue curling.

Electric Currents Produce Magnetic Fields Slide 48 / 162

14 Which diagram shows the magnetic field (red) around a current carrying wire (blue?)

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 49 / 162

15 Which diagram shows the magnetic field (red) around a current carrying wire (blue)?

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 50 / 162

16 Which diagram shows the magnetic field (black) around a current carrying wire (red)?

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 51 / 162

17 Which diagram shows the magnetic field inside and

• utside a current carrying loop of wire?

A B C D

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

. . . . . . . . . . . . . .

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 52 / 162

18 Which diagram shows the magnetic field around a current carrying wire?

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 53 / 162

19 Which diagram shows the magnetic field around a

current carrying wire?

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 54 / 162

20 Which diagram shows the magnetic field inside and

• utside a current carrying loop of wire?

A B C D

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 55 / 162

21 Which diagram shows the magnetic field around a

current carrying wire?

A B C D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 56 / 162

Earlier, it was stated that when a magnet is cut in half, and those pieces are cut in half and this is continued all the way down to the atomic level, then each piece would still have a north and south pole. It is now time to explain why this happens. The real explanation requires an understanding of Quantum Mechanics, but we can use some classical concepts to give you a working understanding of it, and one that can lead to Quantum Mechanics.

Magnetic Field Origin Slide 57 / 162

Classically, the Bohr Model of the atom shows electrons

• rbiting the nucleus. Current, which is made up of moving

electrons, generates a magnetic field. Another contribution to the magnetic field of the atom is a thing called "electron spin." Since the electron is a point particle, it really isn't spinning at all - this is an effect explained by Quantum Electrodynamics. This spin factor adds to the strength of the magnetic field created by the orbital motion of the electrons. So each atom is acting as a magnet with a north and south pole.

Magnetic Field Origin Slide 58 / 162

The magnetic moment (or magnetic dipole moment) of a magnet or an atom or electron is pointed in the direction of the north pole of the object, and represents the strength of the magnetic field produced by the object. It is a measure of how strongly it will interact with an external magnetic field.

Magnetic Moment

• r

Using the Bohr model, we have an electron traveling clockwise, which means we have a current going counter clockwise. μ represents the direction and strength of the magnetic moment.

Slide 59 / 162 Magnetic Field Origin

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the letters above the two arrows.

The arrows in the below diagrams represent atoms and their magnetic fields - with the arrow head the north pole and the other end the south pole (their magnetic moments). Each group of like pointed arrows is called a Magnetic Domain. In a magnetic domain, each atom has its magnetic moment in the same direction. What do you think is happening below? which picture could be a permanent magnet? Which could be a piece of plastic?

Slide 60 / 162 Magnetic Field Origin

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the letters above the two arrows.

For a random group of atoms, there is no real reason for their magnetic poles to align. The picture on the left shows a pretty random ordering of magnetic field directions - with aligned fields

• nly in each magnetic domain.

Looking at the left picture as a whole, the various magnetic fields cancel out - so it would not be a very good magnet in this state. It could be a piece of plastic.....or a certain type of metal that could become a magnet with the application of an external magnetic field.

Slide 61 / 162 Magnetic field Origin

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the letters above the two arrows.

As you move from left to right, more of the magnetic field lines are in the same direction - the middle picture shows a large domain in the middle where the field arrows are all pointing up. Finally, in the third picture, all of the field lines point up, and you could visualize it as a bar magnet with the north pole facing up.

Slide 62 / 162

22 The magnetic field produced by an atom is caused by: Select two answers. A the movement of the protons. B the movement of the electrons. C the electron "spin." D the proton "spin."

Slide 63 / 162

23 An area within a material where all the magnetic moments are pointed in the same direction is called a: A moment of inertia B magnetic force C magnetic domain D magnetic field

Slide 64 / 162

24 What vector measures the ability of an atom to interact with an external magnetic field? A electron orbital velocity B electron spin C magnetic inertia D magnetic moment

Slide 65 / 162 Types of Magnetic Materials

· Ferromagnetic - these materials can be permanently magnetized by the application of the field - all of their domains will line up in the same direction. Examples include: iron, nickel and cobalt. · Paramagnetic - the material weakly interacts with the external field and temporarily lines up some of their domains, so they are attracted to magnets. When the field is removed, the domains resume their random ordering. Examples: magnesium and lithium. · Diamagnetic - another weak, temporary effect, but in this case the domains line up opposite the external field, so these materials are repelled by a magnet. Examples: bismuth and antimony. When you apply an external magnetic field to materials, they respond in three ways:

Slide 66 / 162 Magnetic Domains and Information

By precise applications of magnetic fields, you can encode information on to proper magnetic materials - this is the basis

• f recording music and voice onto magnetic media such as

cassette tapes and the magnetic strips on credit cards. Can you see how the below configuration could store information?

Slide 67 / 162

25 An external magnetic field, in the up direction, is applied to a material with randomly oriented domains. Which of the following represent a ferromagnetic material's response to the external field? A A B B C C

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the arrows, adding a B field and labeling.

A B C

Bexternal Bexternal Bexternal

Slide 68 / 162

26 An external magnetic field, in the up direction, is applied to a material with randomly oriented domains. Which of the following represent a paramagnetic material's response to the external field? A A B B C C

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the arrows, adding a B field and labeling.

A B C

Bexternal Bexternal Bexternal

Slide 69 / 162

27 An external magnetic field, in the up direction, is applied to a material with randomly oriented domains. Which of the following represent a diamagnetic material's response to the external field? A A B B

A B C

Bexternal Bexternal

By The original uploader was 4lex at Spanish Wikipedia (Transferred from es.wikipedia to Commons.) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia

• Commons. File modified by removing the arrows, adding a B field and labeling.

Bexternal

B

C C

Slide 70 / 162

28 A compass needle is made of ferromagnetic materials such as Iron. Why is this advantageous for use in a compass?

Students type their answers here

Slide 71 / 162

29 You have a bar magnet, and you pick up one iron paper

• clip. You then move the magnet/paper clip combination
• ver a group of paper clips, and they get pulled up until

you have a chain of clips. You then try the same experiment with a group of thin copper wires. None of them move. Explain why the iron paper clips were attracted to the magnet and each other, and why the copper wires were unaffected.

Students type their answers here

Slide 72 / 162

Magnetic Field force on a moving Electric Charge

Return to Table

• f Contents

Slide 73 / 162 Magnetic Field force on a moving Electric Charge

Not only do magnetic poles exert a force on each other, but a magnetic field will exert a force on a moving charge. If the charge is not moving - it does not feel the force. This is a very unique concept and phenomenon in the universe. The force on a moving charge is related to the magnitude of its charge, velocity and strength of the magnetic field - but only the portion of the magnetic field that is perpendicular to the charge's

• motion. This will become clearer in AP C Physics, but for now,

here's the equation: F = qvBperpendicular

Slide 74 / 162 Magnetic Field force on a moving Electric Charge

The direction of the force on a positive charge is perpendicular to both the direction of the charge's velocity and the magnetic field. It is found by putting your forefinger (or all four fingers) in the direction of the charge's motion, then curling your fingers in the direction of the magnetic field. The thumb will point in the direction of the magnetic force. NOTE: if the velocity of the charge is in the same or opposite direction as the magnetic field - there is no force on the charge.

Slide 75 / 162 Force on a Moving Charge

v (velocity)

B

v (velocity) Here, we have the case of a negative charge and a positive charge moving to the right in a uniform magnetic field that is pointed out of the page. Use the right hand rule to find the force on the positive charge. Use the same method for the negative charge, but then flip the direction of the resultant force.

Slide 76 / 162 Force on a Moving Charge

v (velocity)

B

v (velocity) F F The direction of the magnetic force is opposite for negative and positive charges. Also, the magnetic force is perpendicular to both the charge's velocity and the direction of the magnetic field. F

Slide 77 / 162 Circular Motion

Since the magnetic force is perpendicular to the charge's velocity, we have a "center seeking" force, which results in centripetal motion - the charge moves in a circle. An electron injected with velocity, v, into the magnetic field on the right will have a magnetic force directed to the right at all times (towards the middle of a circle). A positive particle will move in a counter clockwise path.

Slide 78 / 162 Circular Motion

Circular motion was covered in the mechanics section of this course. Looking at the diagram on the right, can you see the relationship to the gravitational force? It could be a planet moving around the sun. What happens to the speed of the planet as it orbits? Predict what happens to the speed of the charged particle in a magnetic field.

Slide 79 / 162 Circular Motion

For a planet in a gravitational field, the force is always perpendicular to the motion of the planet. Thus, no Work is done on the planet and its speed stays constant. The same is true for a charged particle moving in a magnetic field. In both cases the velocity changes constantly (its direction keeps changing), but its speed is constant. At the end of this chapter, we will see a practical use for this configuration.

Slide 80 / 162 Motion due to a Horseshoe Magnet

If a charge is injected with a velocity from right to left, can you show why the charge will experience a force away from the magnet? Later, we'll show how this principle can be used in motors and stereo speakers! If you take a bar magnet and bend it in the middle and make a U shape, you get a Horseshoe magnet - and it gives a very nice uniform magnetic field between the two poles, pointing from the North to the South pole.

Slide 81 / 162

30 A proton moving at a speed of 75,000 m/s horizontally to the right enters a uniform magnetic field of 0.050 T which is directed vertically downward. Find the direction and magnitude of the magnetic force on the proton.

Slide 82 / 162

31 An electron experiences an upward force of 2.8x10-12 N when it is moving at a speed of 5.1x106 m/s towards the

• north. What is the direction and magnitude of the

magnetic field?

Slide 83 / 162

32 What is the direction of the force on a proton moving to

the right, with speed v, as shown below?

A B C D E

v zero

Slide 84 / 162

33 What is the direction of the magnetic force on the proton

below?

Zero A B C D E F

v

Slide 85 / 162

34 What is the direction of the magnetic force on the

electron below?

Zero A B C D E F

v

Slide 86 / 162

35 What is the direction of the magnetic force on the

electron below?

A B C D E F G Zero

v Slide 87 / 162

36 What is the direction of the magnetic force on the

electron below?

A B C D E F G Zero

v Slide 88 / 162

37 What is the direction of the magnetic force on the proton

below?

A B C D E F G Zero

v Slide 89 / 162

Magnetic Field force on a current carrying wire

Return to Table

• f Contents

Slide 90 / 162 Magnetic Field Force on a current carrying wire

Instead of just examining what happens to a moving charge in a magnetic field, let's take a constant flow of charges - a current - in a wire and see what happens. Each charge will feel a magnetic force. So you would expect the wire in which the charges move would feel a force in the same direction. Look at the picture to the right - the wire is in red. What are the magnetic forces on the three segments of the wire (horizontal, left vertical, right vertical) in the magnetic field?

Slide 91 / 162 Magnetic Field Force on a current carrying wire

The direction is given by the right hand rule again - but, this time, place your fingers in the direction of the conventional current, then curl them into the magnetic field (just like you did for the moving charge). Your thumb will point in the direction of the force. This is a little different from when we found the magnetic field around a current carrying wire - in that case, your thumb was in the direction of the current, and your curling fingers described the magnetic field direction.

Slide 92 / 162 Magnetic Field Force on a current carrying wire

Since the current in the vertical segments of the wire are parallel to the magnetic field, they feel no force. The horizontal segment feels a force directed away from the magnet. The battery supplying the current is now drawn

• n the diagram. Picture the two dots as pivot

points for the wire. What will happen to the current loop?

Slide 93 / 162 Magnetic Field Force on a current carrying wire

It will start to rotate about the black horizontal bar at the top, before gravity pulls it back. Then it will feel the magnetic force again and rotate up and it will keep moving in this pattern! This is the beginning of how you would take electric current, a magnet, and start something rotating. What have we just "invented?"

Slide 94 / 162 Magnetic Field Force on a current carrying wire

This is the beginning of a motor! There is much more that you have to do from an engineering perspective to make a real

• motor. Having a loop just go up and down

isn't very valuable. Either in class now, or for homework, look up how this configuration would be changed to make a real motor. And while you're at it....you probably know that the ear buds from your cell phone have a tiny magnet in them. Look up "how do music speakers work" and see how this model works for producing music.

Slide 95 / 162

The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation. I is the current L is the length of wire B is the magnetic field (perpendicular to both the force and current)

Magnetic Field Force on a current carrying wire

F = ILBperpendicular

Slide 96 / 162

38 If the battery is disconnected from the configuration below, what will be the motion of the wire loop? Explain.

Students type their answers here

Slide 97 / 162

39 A 0.5 m long wire carries a current of 2.0 A in a direction perpendicular to a 0.3 T magnetic field. What is the magnitude of the magnetic force acting on the wire?

Slide 98 / 162

40 A uniform magnetic field exerts a maximum force of 20 mN on a 0.25 m long wire, carrying a current of 2.0 A. What is the strength of the magnetic field?

Slide 99 / 162

41 A 0.050N force acts on a 10.0 cm wire that is perpendicular to a 0.30 T magnetic field. What is the magnitude of the electric current through the wire?

Slide 100 / 162

42 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)?

zero

A B C D E F G

Slide 101 / 162

43 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)?

zero

A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 102 / 162

44 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)?

zero

A B C D E F G

Slide 103 / 162

45 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)?

zero

A B C D E F G

Slide 104 / 162

46 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 105 / 162

47 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 106 / 162

48 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 107 / 162

49 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 108 / 162

50 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 109 / 162

51 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 110 / 162

52 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 111 / 162

53 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 112 / 162

54 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 113 / 162

55 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 114 / 162

56 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 115 / 162

57 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 116 / 162

58 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 117 / 162

59 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 118 / 162

60 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 119 / 162

61 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 120 / 162

62 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Slide 121 / 162

63 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 122 / 162

64 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 123 / 162

65 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 124 / 162

66 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 125 / 162

67 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 126 / 162

68 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 127 / 162

69 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 128 / 162

70 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 129 / 162

71 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 130 / 162

72 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 131 / 162

73 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 132 / 162

74 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 133 / 162

75 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 134 / 162

76 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 135 / 162

77 What is the direction of the magnetic force on the current

carrying wire (green) in the magnetic field (red)? zero A B C D E F G

Slide 136 / 162

Magnetic Field due to a long straight current carrying wire

Return to Table

• f Contents

Slide 137 / 162 Magnetic Field Due to a Long Straight Wire

It was determined experimentally by Oersted, Ampere and others that the magnetic field decreases as the distance, r, increases away from the wire. The Biot-Savart Law and Ampere's Law (which will be done in AP C Physics) both calculate this value: The constant μ0 is called the permeability of free space, and has the value: The constant μ0 is the magnetic equivalent of the electrical constant,ℇ0, which is the permittivity of free space.

Slide 138 / 162 Permeability of Free Space

The permeability of free space, μ0, is a constant that relates the magnetic field produced by a current or a moving electric charge in a vacuum to the value of the current. It will have different values for different media. Did you notice that when you solve for B, using the equation on the previous page, you don't even have to use π? The value of μ0 and the geometry of the problem enable us to just cancel out π.

Slide 139 / 162

78 What is the magnetic field at a point 0.50 m away from a wire carrying 40.0 A of current?

Slide 140 / 162

79 A long straight wire carries a current of 12 A towards the west (left). What is the direction and magnitude of the magnetic field 10.0 cm to the south (below) the wire?

Slide 141 / 162

80 A straight wire with a current of 50.0 A is oriented

• vertically. What is the magnitude of the magnetic field at

a point 2.0 m away from the wire?

Slide 142 / 162

81 A long straight wire carries a current of 30.0 A towards the west (left). What is the direction and magnitude of the magnetic field 5.0 m to the north (above) the wire?

Slide 143 / 162

Magnetic Field force between two current carrying wires

Return to Table

• f Contents

Slide 144 / 162 Force between Two Parallel Wires

Set up two current carrying wires, each of length L, next to each other. Each wire will create a magnetic field that will exert a force on the

• ther wire. Let's look at the force
• n Wire B due to Wire A.

Since the wires are separated by a distance d, the magnetic field generated by Wire A at Wire B's position is:

Slide 145 / 162 Force between Two Parallel Wires

The magnetic field due to Wire A is everywhere perpendicular to the current in Wire B, so the force on Wire B due to Wire A is: And rearranging: Substitute the value of B

1 found on the

previous slide:

Slide 146 / 162 Force between Two Parallel Wires

We can carry out a similar analysis for the force that wire B exerts on wire A or, we could just use Newton's Third Law (it also works on magnetic and electrical forces) to state that the magnitudes of the two forces are equal.

Slide 147 / 162

Parallel currents in the same direction attract. Parallel currents in opposite directions (antiparallel) repel. B2 B2 B1 B1

X X

B2

X

B2 B2

X

B1

Force between Two Parallel Wires

Using the right hand rule, the directions of B1 and B2 for both of the situations to the right are shown. Then, the directions of the force on both wires are found by the right hand rule.

Slide 148 / 162

82 What is the magnitude and direction of the magnetic force between two parallel wires, 5.0 m long, 2.0 cm apart, if each carries a current of 15 A in opposite directions?

Slide 149 / 162

83 Two parallel wires with currents flowing in opposite directions at 5.8 A and 3.2 A are separated by a distance

• f 12 cm. The length of the wires is 9.6m. What is the

magnitude and direction of the magnetic force beween the wires?

Slide 150 / 162

84 What is the magnitude and direction of the magnetic field force between two parallel wires 0.50 m long and 1.0 cm apart if each carries a current of 0.25 A in the same direction?

Slide 151 / 162

Mass Spectrometer

Return to Table

• f Contents

Slide 152 / 162 Mass Spectrometer

Now that electric and magnetic fields have both been presented, it is time to show an application that uses both types of fields. A Mass Spectrometer is used to separate out atoms and molecules based on their mass - and is used to analyze the physical makeup of substances in terms of their relative concentrations of their constituent parts.

Slide 153 / 162 Mass Spectrometer

This is the first part of a Mass Spectrometer - the Velocity Selector. The substance to be analyzed is charged and injected into the left side of the Velocity Selector. An Electric field is directed vertically up, and a Magnetic Field is perpendicular to it and directed out of the page. Velocity Selector There is a slit at the right side which only allows particles that are undeflected by the two fields to pass through.

Slide 154 / 162 Mass Spectrometer

FE FB

Here is the free body diagram and the balanced force equation for a particle to go straight through the selector (Zero acceleration in the up/ down direction). Only particles with a velocity v=E/B will pass straight through - hence the name "Velocity Selector." Velocity Selector

Slide 155 / 162

The second part of the Mass Spectrometer is a semicircle, with a magnetic field again pointing out of the page, and of the same magnitude as the magnetic field in the velocity

• selector. Atoms reaching the

second magnetic field will have the same speed because of the velocity selector. What happens to the speed of the atoms once they're in the semicircle? Think back to the earlier chapter on motion of charges due to a magnetic field.

Mass Spectrometer Slide 156 / 162

The magnetic field in stage 2 will exert a centripetal force on the charges entering it. The force is perpendicular to the atoms' motion at all times, so no work is done on the atoms, and their speed stays constant.

Mass Spectrometer

Slide 157 / 162

Here are the equations to solve for the mass of the atoms:

Mass Spectrometer

Newton's Second Law Magnetic Field Force Solving for m v=E/B from velocity selector The various masses will separate out along the diameter of the semicircle and are calculated by the above equation.

Slide 158 / 162

85 How does the velocity selector in a Mass Spectrometer

• nly allow charged particles with a specific velocity to

exit?

Students type their answers here

Slide 159 / 162

86 What happens to the speed of a charged particle that is injected into an area that just has a magnetic field? Select two answers. A It remains the same. B The field does no work on the charge. C It increases. D The field does positive work on the charge.

Slide 160 / 162

87 A proton (q=1.6x10-19 C) with a velocity of 2.0 x 104 m/s is inserted into the semicircle that has a magnetic field of 5 x 10-3 T. How far from the injection point does the proton strike? The mass of a proton is 1.67 x 10-27 kg.

proton detector

Slide 161 / 162 Summary

· Magnets have North and South poles. · Like poles repel, unlike poles attract each other. · Unit of magnetic field: Tesla=10 4 Gauss. · Electric currents produce Magnetic fields · A magnetic field exerts a force on a moving charge: F = qvBperpendicular · A magnetic field exerts a force on an electric current: F = ILB perpendicular · Magnitude of the field of a long, straight current-carrying wire: · Parallel currents attract; antiparallel currents repel Return to Table

• f Contents

Slide 162 / 162