Ch28 Magnetic Field

8/8/2019 Ch28 Magnetic Field

1/27

Fall 2008: ICE 0116

General Physics II

Ch. 28 Magnetic field

Instructor: Prof. Kondekar Pravin N

Information and Communications University

Text: Fundamentals of Physics (8th

ed.) by Halliday, Resnick, Walker


2/27

-2-Kondekar SchoolofEngineering, ICU

Topics

The magnetic field (B )

The Hall effect

A circulating charged particle

Magnetic force on a current-carrying wire

Torque on a current loop

The magnetic dipole moment


3/27


The magnetic field

Magnets and electromagnets We know about magnetic forces produced by

Static charges produce and feel electric forces.

Moving charges produce and feel magnetic forces too.

In magnets, the moving charges are the electrons in the atoms that make thematerials.

In electromagnets, they are the charges that make up the current in the wire.

magnets

electromagnets


4/27


The magnetic field

No magnetic monopoles The situation is very similar to electrostatics, if we substitute poles

where we used to say charge : like poles repel, opposite poles attract.

However : no isolated poles occur in nature. They all occur in pairs. Cut amagnet in half, you still have two magnets with two poles each!


5/27


The magnetic field

Magnetic fields We define magnetic fields and magnetic field lines in the same way we did for

electric fields. The magnetic field lines of a magnet are very much like that ofelectric dipole :

Magnetic field lines go from north pole to south pole(on the outside). However,

magnetic field lines are always closed: there are no monopoles where the linescan end! So, that go from south to north in the inside.

The earth has a magnetic field too: this is the magnetoshere.


6/27


The definition of B

Units of magnetic field Tesla, (Gauss=10-4T)

Magnetic field in nature

Well-shielded lab : ~10-14T

Earths surface : ~100T(1G)

Fridge magnet : ~10mT(100G)

Electromagnet : ~1T(10kG)

Superconducting NMR magnet : ~2T

Superconducting lab magnet : 10T-20T

High magnet field lab(e.g. Los Alamos) : 30T-60T

Neutron star : 100MT

mA

N

meterondcoulomb

newton

ondmetercoulomb

newtonTtesla

!

!

!!

1

))(sec/(1

)sec/)((111


7/27


The definition of B

Force exerted by magnetic field Observations of MOVING charges show the presence of a velocity-dependent

FORCE that is given by :

We attribute such a force to a MAGNETIC FIELD = B

Units of B : Tesla =(N.s)/(C.m)=N/(A.m)

Compare with for electric fields : definition of fields!EqF!

BvqF v!

Newtons Coulombs Meter/second


8/27


Magnetic and electric forces

Right hand rule

The force acting on a charges paticle moving with velocity though amagnetic field is always perpendicular to and .

BF v

v BB


9/27



Magnetic and electric force

Charges thatdo not move, do not feel magnetic force (what about magnets?)

Magnetic forces are perpendicular to both the velocity of charge and to themagnetic field (electric forces are parallel to the field). Since magnetic forcesare perpendicular to the velocity they do not work

Speed of particles moving in a magnetic field remains constant in magnitude,the direction changes. Kinetic energy is constant (no work)

EqF !For electrostatic forces :

For magnetic forces : BvqF v!


10/27



Example An electron is traveling with a constant velocity v.

It enters a box in which there is a uniformmagnetic field B.

Which of the following is TRUE?

(a) The electron speeds up.

(b) The electron slows down.

(c) The electron speed is constant.

(d) It depends on the direction of themagnetic field.

Force is qv x B

Direction of force is ALWAYSnormal to velocity! Speed CANNOT CHANGE! Direction of velocity DOESCHANGE i.e. acceleration is NOT 0!


11/27



Sample problem Uniform magnetic field : , Kinetic energy : 5.3 MeV

Magnetic deflecting force ?

mTB 2.1!

s

kg

MeVJMeVKv

mvK

/102.3

1067.1

)/1060.1)(3.5)(2(2

2

1

7

27

13

2

v!

v

v!!

!

N

vBqFo

B

15101.6

90sin

v!

!

212

27

15

/107.31067.1

101.6sm

kg

N

m

Fa B v!

v

v!!


12/27


Crossed fields : discovery of the electron

Experiment Discovery of the electron in 1897 by J. J. Thomson

Ions are injected in the region of crossed E and B fields, which fixedtheir velocity

Electric field (perpendicular) electric force: (perpendicualar)

Magnetic field(horizontal) magnetic force (perpendicular)

EeBev


13/27


Crossed fields : discovery of the electron

e/m of electron E = 0, B = 0 : note the position of the spot on screen S due to the

undeflected beam

E 0, B = 0 : Measure the resulting beam deflection (perpendiculardirection)

E 0, b 0 and adjust its value until the beam returns to theundeflected position

2

2

2mv

eEL

y !

yE

LB

e

m

B

E

vevBeE 2

22

!!!

),1913,106.1( 19 MillikanInCe

v!


14/27


Crossed fields : Hall effect

Hall effect In 1879, Edwin H. Hall

Copper strip of width d in crossed field


15/27


Crossed fields : Hall effect

Hall effect Hall potential difference V

Different charge (negative or positive) the opposite direction

Number density

The electric and magnetic forces are in balance

Drift speed

Number density

Ed!

BeveE d!

neA

i

ne

Jvd !!

le

Bin ! )/( dAl!


16/27


Crossed fields

Example In the boxed region:

Uniform Balong -y

Uniform Ealong +z

An electron (me, -e) enters atleft with velocity v along +x

Can the electron travel throughthe box undisturbed, as shown?

(a) No, this is impossible!

(b) Yes, if v = (eB)/E

(c) Yes, if v = E/BForce on electron due to E is along -z (intopage)Force on electron due to B is along +z(out of page) Balance these out: eE = evB [sin(900) = 1] v = E/B


17/27



Circular motion Since magnetic force is transverse

to motion, the natural movementof charges is circular.

The radius of the circular path

Period T

qB

mvr

r

mvqvB

rvmF

!!

!

2

2

m

qBf

m

qB

Tf

qB

m

v

r

T

!!

!!

!!

T[

T

TT

2

2

1

22


18/27



Helical paths If the velocity of a charged particle has a component parallel to the (uniform)

magnetic field, the particle will move in a helical path about the direction ofthe field vector.


19/27



Sample problem (mass spectrometer) B = 80.000mT, V = 1000.0V , q = +1.6022 X 10-19C, x =1.6254 m

q

mV

Brx

q

mV

Bm

qV

qB

m

qB

mvr

mqVv

qVmv

UK

222

212

2

02

1

0

2

!!

!!!

!

!

!((

ukgqxB

m 93.203103863.38

25

22

!v!! )106605.11( 27kgu v!


20/27


Cyclotrons and synchrotrons

The cyclotron Suppose you wish to accelerate

charged particles as fast as you can

The proton synchrotron

Linear accelerator (long)

)( conditionresonanceffosc

!

oscfmqB T2!


21/27


Cyclotrons and synchrotrons

Sample problem Cyclotron, oscillator frequency : 12MHz, a dee radius R=53cm

(a) Magnetic field? m=3.34 X10-27kg

(b) Kinetic energy?TT

C

skg

q

mfB osc

6.157.1

1060.1

)1012)(271034.3)(2(219

16

}!

v

vv!!

TT

J

smkg

mvK

sm

kg

Tm

m

RqBv

12

2727

2

7

27

107.2

)/1099.3)(1034.3(2

1

2

1

/1039.3

1034.3

)57.1)(191060.1)(53.0(

v!

vv!

!

v!

v

v!!


22/27



Magnetic force on a wire

Note : if wire is not straight, compute force ondifferential elements and integrate

BvqF

v

Liitq

d

d

v!

!!

BiLBq

iLqF v!v!

B

LiF

v!

BLid

Fd v!


23/27



Sample problem i=28A, linear density of the wire : 46.6 g/m

What are the magnitude and direction of theminimum magnetic field needed to suspend thewire-that is, to balance the gravitational force on it

B

T

A

smmkgB

i

gLm

iL

mgB

mgiLB

2

23

106.1

28

)/8.9)(/106.46(

)/(

sin

sin

v!

v!

!!

!

J

J


24/27


Torque on a current loop

Rectangular coil : a x b, current = i

Net force on current loop = 0

But : Net torque is NOT zero!

For a coil with N turns

iaBFF !!31

UX sin)( BNiA! (WhereA is the area of coil)

UUX sinsinTorque 11 iabBbFbF !!v!!


25/27



Magnetic moment We just showed : Define : magnetic dipole moment

The coil behaves like a bar magnet placedin the magnetic field

Current carrying coil: magnetic dipole

As in the case of electric dipoles magneticdipoles tend to align with the magnetic field

UX sinNi B!

^

)( nNi!Q

Bv! QX

Right hand rule : curl fingers in

direction of current : thumb

points along


26/27



Electric and magnetic dipoles

Epv!X Bv!X

EpU !)(UBU ! QU )(


27/27



Example

Ch28 Magnetic Field

Documents

Transcript of Ch28 Magnetic Field