phys632 l8 ch 28 mag field 10

7/29/2019 PHYS632 L8 Ch 28 Mag Field 10

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Lecture 8 Magnetic Fields Ch. 29

Cartoon Magnesia, Bar Magnet with N/S Poles, Right Hand Rule

Topics

Permanent magnets

Magnetic field lines,

Force on a moving charge,

Right hand rule,

Force on a current carrying wire in a magnetic field,

Torque on a current loop

Demos Compass, declinometer, globe, magnet

Iron fillings and bar magnets

Compass needle array

Pair of gray magnets

CRT illustrating electron beam bent bent by a bar magnet - Lorentz law

Gimbal mounted bar magnet

Wire jumping out of a horseshoe magnet. Coil in a magnet

Elmo

Polling


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\


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Magnetic Fields

Magnetism has been around as long as there has been an Earth with

an iron magnetic core.

Thousands of years ago the Chinese built compasses for navigation inthe shape of a spoon with rounded bottoms on which they balanced

(Rather curious shape for people who eat with chopsticks).

Certain natural rocks are ferromagnetic having been magnetized by

cooling of the Earths core.

Show a sample of natural magnetic rock. Put it next to many

compasses.


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Magnetisms Sociabilities

Magnetism has always has something of a mystic aura about it. It is

usually spoken of in a favorable light.

Animal magnetism, magnetic personality, and now you can wear

magnetic collars, bracelets, magnetic beds all designed to make you

healthier even grow hair.

We do not have the same feeling about electricity. If you live near

electric power lines, the first thing you want to do is to sue the electric

company.


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Compass and Declinometer

In 1600 William Gilbert used a compass needle to show how it orienteditself in the direction of the north geographic pole of the Earth, which

happens to be the south magnetic pole of the Earths permanentmagnetic field.

Show compass and declinometer. Each has a slightly magnetizedneedle that is free to rotate. The compass lines up with the componentof the magnetic field line parallel to the surface of the Earth. Thedeclinometer lines up with the actual magnetic field line itself. It saysthat the angle between the field lines and the surface is 71 degrees asmeasured from the south.

Earths magnetic field

Basically there are two types of magnets: permanent magnets andelectromagnets

Show field lines for a bar magnet. Show bar magnet surroundedby compass needle array.


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Permanent Magnets

Bar magnet is a model of a ferromagnetic material that can be

permanently magnetized. Other ferromagnetic materials are

cobalt and nickel.

The origin of magnetism in materials is due mostly to the spinning

motion of the charged electron on its own axis. There is a small

contribution from the orbital motion of the electron.

+

a

v

Electronorbiting

nucleus

Magnetic dipole

Magnetic

dipole

s

Electron

spinning onits axis

e

-

Atomic origin of magnetic field


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Permanent Magnets (continued)

In ferromagnetic materials there are whole sections of the iron

called domains where the magnetism does add up fromindividual electrons. Then there are other sections or domains

where contributions from different domains can cancel.

However, by putting the iron in a weak magnetic field you can

align the domains more or less permanently and produce a

permanent bar magnet as you see here.

In nonmagnetic materials the contributions from all

The electrons cancel out. Domains are not even formed.


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Magnetic field lines donot stop at surface.

They are continuous.

They make completeloops.

Field lines for a bar

magnet are the same as

for a current loop


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Magnetic field lines

Similarities to electric lines

A line drawn tangent to a field line is the direction of the field at thatpoint.

The density of field lines still represent the strength of the field.

Differences

The magnetic field lines do not terminate on anything. They formcomplete loops. There is no magnetic charge on as there was electriccharge in the electric case. This means if you cut a bar magnet in halfyou get two smaller bar magnets ad infinitum all the way down to theatomic level Magnetic atoms have an atomic dipole not a monopoleas is the case for electric charge.

They are not necessarily perpendicular to the surface of the

ferromagnetic material.

AdEfluxElectric

AdBfluxMagnetic

E

B


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Definition of magnetic Field

definition of a magnetic field

The units of B are or in SI units(MKS).

This is called a Tesla (T). One Tesla is a very strong field.

A commonly used smaller unit is the Gauss. 1 T = 104 G

(Have to convert Gauss to Tesla in formulas in MKS)

In general the force depends on angle . This iscalledthe Lorentz Force

qv

FB

)( .s

mC

N

).( mAN

BvqF


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In analogy with the electric force on a point charge, the corresponding

equation for a force on a moving point charge in a magnetic field is:

Magnitude of

Direction of F is given by the right hand rule (see next slide).

If = 90, then the force = and the particle moves in a circle.

v B sin(0o) = 0 F = 0

F B

v

BvqFm

EqFe

sinqvBFm

qvB

If the angle between v and B is = 0, then the force = 0.

Consider a uniform B field for simplicity.

Bv


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Use right hand rule tofind the direction ofF

+Positive Charge

Rotate v into B through the smaller angle and the force F will be in the directiona right handed screw will move.

BvqFm


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Motion of a point positive charge in a magnetic field.

For a + charge, the particle rotates counter clockwise.

For a - charge, the particle rotates counter clockwise.

This means kinetic energy remains constant.

The magnitude of velocity doesnt change.

Then the particle will move in a circle forever.

The B field provides the centripetal force needed for circular motion.

= qvBsin90o

Direction is given by the RHR (right

hand rule)

Magnitude of F = qvB

B is directed into the paper

r

x

x x

x

x

x

F

v

F

v

Fv +

F

v

B

BvqFm

SinceFv andFd, then the magnetic force

does no work on the charge. Work = 0


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Find the radius r and period of motion for a + charge

moving in the magnetic field B. Use Newtons 2nd Law.

What is the period of revolution of the motion?

qvBr

mvmaF

2

qB

mvr

Radius of the orbit

Important formula in

Physics

v

ar

r

va

2

T2r

v

2m

qB period T

Note the period is independent of the radius, amplitude, and velocity. Example of simple

harmonic motion in 2D.

T is also the cyclotron period.

It is important in the design of the cyclotron accelerator. Of course, this is important

because today it is used to make medical isotopes for radiation therapy.

m

qBf

tf

2

1

Cyclotron frequency

v qBr/m

x

x x

x


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Example: If a proton moves in a circle of radius 21 cm perpendicular to a

B field of 0.4 T, what is the speed of the proton and the frequency of

motion?

1

m

qBf

2

f 1.6 1019C (0.4T)

(2) 1.67 1027 kg

f1.6 (0.4)

(6.28) 1.67108Hz 6.1106Hz

Hzf

6101.6

2

m

qBrv

v 1.6 1019C (0.4T) 0.21m

1.67 1027 kg

v 1.6 (0.4) 0.21

1.67108 m

s

8.1106 ms

s

mv 6101.8

v

r

x x

x x

x x

x

x


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Use right hand rule to

find the direction ofF

+

NegativeCharge

Rotate v into B through the smaller angle and the force F will be in the oppositeDirection a right handed screw will move.

BvqFm


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Suppose we have an electron . Which picture is correct?

x

Noyes B

v

F F

x

x

x

x

x

x

x

v


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Example of the force on a fast moving proton due to the earths

magnetic field. (Already we know we can neglect gravity, but can

we neglect magnetism?) Magnetic field of earth is about 0.5 gauss.

Convert to Tesla. 1 gauss=10-4 Tesla

Let v = 107 m/s moving North.

What is the direction and magnitude of F?

Take B = 0.5x10-4 T and v perpendicular B to get maximum effect.

T105.010C106.1qvBF 4s

m719

m

N108F 17m

(a very fast-moving proton)

metervolts19 100C106.1qEF

e

Fe 1.6 1017N

V x B is into the

paper (west).

Check with globe

Earth

F i i i if i fi ld


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Force on a current-carrying wire in a uniform magnetic field

When a wire carries current in a magnetic field, there is a force on thewire that is the sum of the forces acting on each charge that is

contributing to the current.

vd is the drift

velocity of the

positive charges.

+

Cross sectional area A of

the wire

ivd

F

L

n = density of positive mobile charges

Number of charges = nAL

orL is a vector in the direction of the current i

with magnitude equal to the length of the wire.

Also

v isperpendicular to B

B (Out of the paper)

F (qv B)(nAL)

F nqvALB Current,i nqvA

iLBF

BLidFd

BLiF


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Show force on a wire in a magnetic field

BLiF

Current

up

Current

down

Drift velocity

of electrons

Torques on current loops


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Torques on current loops

Electric motors operate by connecting a coil in a magnetic field to a current

supply, which produces a torque on the coil causing it to rotate.

P i

a

b

Above is a rectangular loop of wire of sides a and b carrying current Iand is

in a uniform magnetic field B that is perpendicular to the normal n.

Equal and opposite forces are exerted on the sides a. No

forces exerted on b since i is parallel to B

Since net force is zero, we can evaluate torque at any point.

Evaluate it at P. Torque tends to rotate loop until plane is

perpendicular to B.

F iaB

i

B

B

F

F

A=ab = area of loop

B

Normal

b

b sin

Normal

Fbsin iaBbsin iABsin

Multiply by N for N loops NiABsin


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Galvanometer

i di l i ll d


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Magnetic dipole moment is called vec

U

B

Ep-U

Ep

Recall that for Electric dipole moment pNiABsin

NiA

Bsinr

r

rB

How do you define the direction of ?

RHR


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Demo: show torque on current loop (galvanometer)

Can you predict direction of rotation?

Example

A square loop has N = 100 turns. The area of the loop is 4 cm2 and it

carries a current I = 10 A. It makes an angle of 30o with a B field

equal to 0.8 T. Find the magnetic moment of the loop and the torque.

Demo: Show worlds simplest electric motor

(scratch off all insulation on one end)

Scratch off half on the other end

Momentum will carry it turn

(no opportunity for current to reverse coil direction)

mNTmABTmAmANiA

.16.05.08.0.4.030sin.4.010410100

2

224


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Electron moving with speed v in a crossed electric

and magnetic field in a cathode ray tube.

F q

E q

v

B

ye

Electric field bends particle upwards

Magnetic field bends it downwards


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Discovery of the electron by J.J. Thompson in 1897

2

2

mv2

qELy

1. E=0, B=0 Observe spot on screen

2. Set E to some value and measure y the deflection

3. Now turn on B until spot returns to the original position

B

Ev

qvBqE

4 Solve foryE2

LB

q

m 22

This ratio was first measured by Thompson

to be lighter than hydrogen by 1000

Show demo of CRT


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Chapter 28 Problem 18

An alpha particle (q = +2e, m = 4.00 u) travels in a circular path ofradius 5.00 cm in a magnetic field with B = 1.60 T. Calculate the

following values.

(a) the speed of the particle

(b) its period of revolution

(c) its kinetic energy

(d) the potential difference through which it would have to be

accelerated to achieve this energy


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A 2.3 kg copper rod rests on two horizontal rails 2.4 m apart andcarries a current of 60 A from one rail to the other. The

coefficient of static friction between rod and rails is 0.51. What

is the smallest magnetic field (not necessarily vertical) that

would cause the rod to slide?

(a) magnitude and direction


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A circular coil of 130 turns has a radius of 1.50 cm.

(a) Calculate the current that results in a magnetic dipole moment of 2.30Am2.

(b) Find the maximum torque that the coil, carrying this current, canexperience in a uniform 20.0 mT magnetic field.

phys632 l8 ch 28 mag field 10

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