Notes.intro.magnetism

7/30/2019 Notes.intro.magnetism

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Magnetism

Introduction to Magnetism

The study of classical physics is divided into five parts:

Mechanics

Thermodynamics Electricity and Magnetism (E/M)

Waves, Sound, and Light

Atomic and Nuclear Physics

Electricity was divided into two main topics:

Electrostatics: the study of charges at rest

Electric Circuits: the study of charges in motion

Magnetism is also divided into two parts:

Magnetostatics: the study of constant magnetic fields (Chapter 20)

Electromagnetic Induction: the study of magnetic fields that change with time (Chapter21)

These are the final two chapters of electricity and magnetism. In this chapter, we will be

introducing the magnetic force and the magnetic field. This chapter deals with magnetostatics or

magnetic fields that do not change with time.

This chapter is broken down into four lessons:

Magnetism and Magnetic Fields Forces acting on Moving Charges

Forces acting on Current-Carrying Wires Magnetic Fields around Current-Carrying Wires

Lesson 1: Magnetic Fields and Forces on Moving Particles

History of Magnetism

(From: http://www.sciencetech.technomuses.ca/english/schoolzone/Info_Magnets.cfm)

The history of magnetism began many, many years ago. Legend has it that an elderly shepherdnamed Magnes was herding his sheep in an area of Northern Greece called Magnesia about

4,000 years ago. It is said that the nails in his shoes and the metal tip of his staff became firmly

stuck to the large, black rock on which he was standing. This type of rock was subsequentlynamed magnetite, after either Magnesia or Magnes himself.
http://www.sciencetech.technomuses.ca/english/schoolzone/Info_Magnets.cfmhttp://www.sciencetech.technomuses.ca/english/schoolzone/Info_Magnets.cfm


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Magnetism

Stories of magnetism date back to the first century B.C. For many years following its discovery,

magnetite was surrounded in superstition and was considered to possess magical powers, such as

the ability to heal the sick, frighten away evil spirits, and attract ships made of iron! Unlikeamber (fossilized tree resin), magnetite was able to attract objects without first being rubbed (as

we learned in electrostatics). This made magnetite even far more magical. People soon realized

that magnetite not only attracted objects made of iron, but when made into the shape of a needleand floated on water, magnetite always pointed in a north-south direction creating a primitive

compass. This led to an alternative name for magnetite ~ lodestone ~ meaning "leading stone".

Only iron and a few other materials, such as cobalt, nickel, gadolinium, and some of their oxides

and alloys show strong magnetic effects. All of these substances are said to be ferromagnetic ~that is, possessing magnetic effects. Objects made out of ferromagnetic materials are called

magnets.

So we have known for a long time that magnets produce magnetic effects. It was not until the

1800s, however, that we learned that electric currents also produce magnetic effects. This was a

grand discovery for it tied together both electricity and magnetism. This realization also furtherfueled the thought that all of physics is closely intertwined and that a Grand Unification Theory

probably exists. Much of the research in modern physics today centers on trying to tie gravity tothe concepts of electricity and magnetism. Perhaps there will be a physics breakthrough in your

lifetime!

In real life, the many practical devices depends on the effects of magnetism: from compasses to

motors, loudspeakers, computer memory, MRI scans, and electric generators.

In Summary: What causes magnetic effects?

Magnets Electric currents

What do we know about magnets?

Magnets have a north pole and a south pole

Like poles repel, unlike poles attract

There is no magnetic monopole meaning that you cannot create just a north pole

or just a south pole. If you cut a magnet in half, you will have a smaller magnet with both

a north and south pole.


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Magnetism

What is a magnetic field?

The magnetic field is the space around a magnet in which magnetic forces are present.

The symbol for the magnetic field is B. The strength of the magnetic field is measured in Teslas (T). One Tesla is also equal to 1

Weber per meter squared (1 T = 1 Wb/m2). The Weber will be used in the next chapter.

Magnetic field is a vector. The magnetic field has both a magnitude and a direction.

We will learn how to calculate the magnitude (strength) of the magnetic field in Lesson 4.

( oI

B2 r

=

)

We use right-hand rules to determine the direction. (Part of this lesson is to learn the

right-hand rules.)

What does the magnetic field look like?

For the AP test, you should know what the magnetic field around a bar magnet and horseshoemagnet look like. Even the Earth can be thought of as a simple bar magnet!

The direction of the magnetic field at any point is defined as the direction in which the north poleof a compass would point.

Furthermore, the magnetic field can be visualized with magnetic field lines. Lining up theneedles of multiple compasses or sprinkling tiny iron filings around a magnet allows us to see the

shape of the magnetic field.


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Magnetism

Facts about Magnetic Field Lines

Magnetic field lines always point from the north pole toward the south pole of a bar

magnet

Magnetic field lines within a horseshoe magnet are practically parallel. There the

magnetic field strength within the horseshoe magnet is constant.

Magnetic field lines continue inside a magnet to form continuous loops

The more closely spaced the lines, the greater the magnetic field strength

The direction of the magnetic field is tangent to a field line at any point


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Magnetism

The Earths Magnetic Field (just interesting stuff!!)

There is also a magnetic field around the Earth. The magnetic field is shaped as if there was a bar

magnet inside the Earth. The Earth's magnetic field is slightly tilted with respect to the planet'sspin axis. Therefore, the Geographic North Pole and the Magnetic North Pole are not actually in

the same place. There is currently an 11-12 difference between the two. Compasses pointtoward the Magnetic North Pole not the Geographic North Pole. So if youre using a compass tofind Santas Workshop, you may get lost!

Even more interesting, the magnetic north and south poles of the Earth are continually moving.

Although scientists do not understand all of the details, we know that the Magnetic North Pole

moved approximately 1,100 km (684 miles) during the 20th century. Scientists have alsodiscovered that the strength of the Earths magnetic field has been decreasing slightly ever since

around 1850. Over the course of the Earth's history, the Earth magnetic field has actually

reversed itselfmany times, with the North Pole becoming the South Pole and vice versa!

How to draw magnetic fields on paper

In this chapter, many of the variables act at right angle to one another. As a result, we will be

using the x, y, and z axes. We need to be able to represent the direction of the magnetic field on

paper. We indicate the direction of the magnetic field by a series of arrows. We describe thedirection as +/- x, y, or z. Magnetic field lines in the +z direction point out of the paper. If you

were looking at them, you would see the tips of the arrows. Therefore, the +z direction is

represented by a series of dots (arrow tips). Magnetic field lines in the z direction point into the

paper. If you pretend that the arrows have feathers on them, you would see the x shape of thefeathers. As a result, xs stand for the z direction.

The following are examples of standard conventions:

+x direction -y direction +z direction -z direction

Force that acts on Moving ChargesWhen a charge is placed in an electric field, it experiences a force. (F = qE)

When a charge is placed in a magnetic field, it also experiences a force provided the following

two conditions are met:

The charge is moving. (The magnetic force does not act on stationary charges.)

x x x x x x

x x x x x xx x x x x x

x x x x x x

x x x x x x
http://www.windows.ucar.edu/tour/link=/earth/Magnetosphere/earth_magnetic_reversals.html&text=thttp://www.windows.ucar.edu/tour/link=/earth/Magnetosphere/earth_magnetic_reversals.html&text=t


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Magnetism

The velocity of the charge (or a component of the velocity) is perpendicularto the

direction of the magnetic field.

If these conditions are met, a magnetic force acts on the moving charge.

The equation for the magnetic force is F qvB= where:

q is the magnitude of the charge in Coulombs (C)

v is the velocity of the charge in m/s

B is the strength of the magnetic field in Teslas

The direction of the force is always perpendicular to the direction of the velocity and also

perpendicular to the direction of the B. This means that each of the variables (F, v, an B) all act

perpendicular to one another ~ each residing on the x, y, or z axis.

Because of the three-dimensional nature of this topic, we use right-hand rules to help usdetermine the direction of the variable in question. The perpendicular nature of these variables

and the related right-hand rule are the focus of this lesson.

Direction of the Magnetic Force ~ Right Hand Rules (RHR)

There are really three right-hand rules. We only need to know two of them, however, for this

class so we will pretend that there are only two. There is also little consistency between the rules.

What one book or website calls RHR1, another calls RHR2 or 3. And even more annoying, the

explanation for how to use the rules differs by textbook, website, or person.

I will share with you what I have found to be the easiest method for students to learn. My method

is slightly different than the one described in your book. This is another one of those topics that

is really easy to show you how to do but difficult to explain in words. Here goes I will callthis Right-Hand-Rule #1 or RHR1.

Right-Hand Rule #1: Direction of Force acting on a Moving Charge

RHR1 is used to determine the direction of the magnetic force that acts on a charge movingthrough a magnetic field. We will use the pictures below as example problems. The black

arrows, dots, or xs indicate the direction of the magnetic field; the red arrows show the direction

of the velocity of the particle. We are trying to determine the direction of the magnetic force thatis produced.

Like all topics in electricity and magnetism, right-hand rules are based on what a positive test

charge or a positively-charged particle would do. If you are asked about an electron or a


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Magnetism

negatively-charged particle, just flip your final answer(i.e. +x becomes x, etc). Or you can use

your left hand for negative particles

And a warning to all you lefties out there: I am left-handed and have always struggled with

RHRs because if I dont consciously think about it, I invariably use my left hand!

Lets do Example 4 (below) as we learn the steps of the right-hand rule.

Procedure for using RHR1: (Obviously, use yourRIGHT HAND!!!)

1. Point your fingers in the direction of the velocity of the particle.

(Hold your hand out straight ~ fingers pointing straight out ~ as if you were about to shakesomeones hand. Thumb and fingers should make an L shape.) For Example 4, your fingers

(hand) should be pointing to the left or in the -x direction.

2. You then curl (bend) your fingers in the direction of the magnetic

field. (Keep thumb pointing out.) For Example 4, your fingers should curl towards you or inthe +z direction. Sometimes you have to rotate your hand to curl properly!

3. If you did everything correctly, your thumb will be pointing in the

direction of the magnetic force that acts on the particle. For Example 4, your thumb should

be pointing straight up or in the +y direction.

Note that we used all three dimensions.

velocity: -x

magnetic field: -z

magnetic force: +y

Practice: Try the remaining examples. Check your answers below. Remember, the red shows the

motion of the particle; the black is the direction of the field.

Example 1 Example 2 Example 3 Example 4

Answers: (direction of magnetic force)

v


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Magnetism

Example 1: -x

Example 2: -z

Example 3: +zExample 4: +y

Possible paths of a particle through a magnetic field

Consider a magnetic field acting in the +x direction. (Themagnetic field is shown in blue in the picture below.) Suppose

three positively-charged particles are moving through the field

as shown. Particle 1 is moving parallel to the field, particle 2moves perpendicular to the field, and particle 3 is moving at

some odd angle through the field. Lets look at the force

produced on each of these three possibilities in detail.

Three possible paths through a magnetic field

Note: Blue is field, green is velocity of particle

Case 1: Moving parallel or anti-parallel through a magnetic field

If a charged particle moves parallel or antiparallel through a

magnetic field, no force acts on the particle!! The magnetic forceonly exists when the velocity of the particle is perpendicular tothe magnetic field!!

Path of particle: straight line (particle moves through field

undeflected.)

Case 2: Moving perpendicular through a magnetic field

Example 1: If a charged particle moves perpendicular through a

magnetic field, it experiences a magnetic force equal to F = qvB.

The direction of the force can be found using RHR1. For thisexample, the magnetic force acts in the z direction.

------------------------------------------------------------------------

Example 2: Suppose a charge particle moves in the +x direction

--------------------------------

o o o o o o o

v

a


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Magnetism

through a field that acts in the +z direction. Because v and B are

perpendicular to one another, a magnetic force acts on the particle

as it moves through the field. Using RHR1, the direction of themagnetic force is -y. This direction of this force is drawn in the

diagram to the right in red.

Newtonss second law says that an object will accelerate in thedirection of the net force and that the acceleration is in the same

direction as the net force. The net force acting on this particle is

the magnetic force, F = qvB. (The gravitational force isnegligible.)

So now we have a particle that is moving forward with a constantvelocity that also experiences an acceleration in the y direction.

(I hope this reminds you of projectile motion ~ fired horizontally

from the top of a cliff!!! Yes, we even have projectile motion inMagnetism!!)

Because the magnetic force continues to act on the particle, theparticle ends up traveling in a circular path.

Path of particle: Circle!!!

Clickhere to view a web animation of this example.

o o o o o o o

o o o o o o o

o o o o o o o o o o o o o o

o o o o o o o

Path is clockwise circle!

Radius can be found from:

2

c

2

mvF

r

mvqvB

r

=

=

Case 3: Moving at an angle through a magnetic field

If a charged particle moves through a magnetic field at an angle

, it will also experience a magnetic force. However, only the

component of the velocity that acts perpendicular to the field

affects the force. This component is shown in red in the diagram

to the right. In this example, it is equal to (v sin). In this

equation, F = qvB, v stands for the velocity perpendicular to the

field. So only the y-component can be used in the equation.

Applying RHR1 to the y-component of the velocity, we find that

the magnetic force acts in the z direction.

Determining path of particle: The perpendicular component of the

velocity acts in the +y direction, the force (and therefore theacceleration) acts in the z direction. This produces a vertical,

circular path ~ traveling into the paper at the top of the circle and

coming out of the paper at the bottom of the circle. (I know that is

confusing. It is a three-dimensional model.) The x-component of

Radius of vertical circle

can be found from:
http://physics.uwstout.edu/physapplets/javapm/java/partmagn/index.htmlhttp://physics.uwstout.edu/physapplets/javapm/java/partmagn/index.html


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Magnetism

the original velocity also affects the motion of the particle. The y-

component is responsible for the vertical, circular path. The x-

component of the velocity stretches the circle resulting in ahelical or spiral path!!

Path of particle: helical or spiral path

2

c

2

mvF

r

mvqvB

r

=

=

vx is rate of motion in x-

direction

Work done by magnetic fields

When a charge moves between the plates of a capacitor, the electric field does workon the

charge. (F = qE, V = Ed, and W = qV) Remember, that for work to be done, the object mustmove in the same direction as the force. (W = Fd). A charged object moving between the plates

of a capacitor moves parallel or anti-parallel to the field. In both cases, work is done.

Magnetic fields, however, do no work!!!!! This is because the magnetic force always acts

perpendicular to the velocity of the charge. Therefore, they never act in the same direction!! Thisis a common trick question. W = 0 for magnetic fields!!!!!!!!!!!!!!


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Magnetism

Sample Problems

Solution:

v and B are at right angles, so force exists!

6

F qvB

.00425 (3.6x10 )(862)(B)

B 1. 37 T

=

=

=

Solution:

6

F qvB

F (53x10 )(1300sin55)(1.37)

F .0773 N

=

=

=

v and B are at right angles, so force exists!

19 7

14

F qvBF (1.6x10 )(2x10 )(.01)

F 3.2x10 N

==

=

Direction of force: From RHR1, force acts on positive charge in the +y direction. Therefore,

forces on an electron in the y direction. Motion is a circle as shown in picture below.

Sample Problem1: Particle 1 (below in picture), with a charge of 3.6 C and a velocity of 862m/s, travels at right angles through a uniform magnetic field. If the particle experiences a

magnetic force of .00425 N, what is the strength of the magnetic field?

Sample Problem 2: Particle 2 (above in picture), with a charge of 53 C and a speed of 1300 m/s,moves at an angle of 55 relative to the 1.37 T magnetic field. Calculate the magnetic force

acting on the particle.

Sample Problem 3: An electron travels 2 x 107 m/s in the +x direction in a magnetic field acting

in the z direction. If the magnitude of the field is .01 T, quantitatively describe the motion ofthe electron.


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Magnetism

Radius of circle can be found from centripetal force equation:

2

c

mvF

r=

What provides the centripetal force?? Answer: The magnetic force!!!

2mvqvB

r= (divide both sides by v)

mvqB

r=

31 719 (9.1x10 )(2x10 )(1.6x10 )(.01)

r

r .011 m

=

=

FE = qE and FB = qvB

You should now be ready to do

WA1: Force acting on Moving Charges

Sample Problem 4: It is very common on the AP test to mix electric and magnetic fields. A particle can

be made to pass through these combined fields undeflected (in a straight line) if you set the electricfield equal to the magnetic field. We will be solving this problem on the DB

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Notes.intro.magnetism