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Magnetic field. Chapter 28. Magnetism. Refrigerators are attracted to magnets!. Where is Magnetism Used??. Motors Navigation – Compass Magnetic Tapes Music, Data Television Beam deflection Coil Magnetic Resonance Imaging (MRI) High Energy Physics Research. Cathode. Anode. (28 – 8).

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Magnetic field

Magnetic field

Chapter 28


Magnetism
Magnetism

  • Refrigerators are attracted to magnets!


Where is magnetism used
Where is Magnetism Used??

  • Motors

  • Navigation – Compass

  • Magnetic Tapes

    • Music, Data

  • Television

    • Beam deflection Coil

  • Magnetic Resonance Imaging (MRI)

  • High Energy Physics Research


Cathode

Anode

(28 – 8)


Consider a permanent magnet

N

S

Consider a Permanent Magnet

The magnetic Field B goes from North to South.




A look at the physics

q

  • If the charge is moving, there

  • is a force on the charge,

  • perpendicularto both v and B.

  • F = q vxB

q

A Look at the Physics

There is NO force on

a charge placed into a

magnetic field if the

charge is NOT moving.

There is no force if the charge

moves parallel to the field.


The lorentz force
The Lorentz Force

This can be summarized as:

F

or:

v

q

m

B

q is the angle between B and V



The wire in more detail
The Wire in More Detail

Assume all electrons are moving

with the same velocity vd.

L

B out of plane of the paper


i

.

(28 – 12)


Current loop
Current Loop

What is force

on the ends??

Loop will tend to rotate due to the torque the field applies to the loop.


Magnetic force on a current loop

F=BIL

F

q

L

S

N

B

I

F

F=BIL

Magnetic Force on a Current Loop


Magnetic force on a current loop1
Magnetic Force on a Current Loop

Simplified view:

F=BIL

q

L

d

I

F=BIL


Magnetic force on a current loop torque electric motor
Magnetic Force on a Current Loop Torque & Electric Motor

Simplified view:

F=BIL

q

L

d

I

F=BIL


Magnetic force on a current loop torque electric motor1

F=BIL

for a current loop

q

L

d

I

F=BIL

Magnetic Force on a Current LoopTorque & Electric Motor


Side view

Top view

C

C

(28 – 13)


Magnetic force on a current loop torque magnetic dipole
Magnetic Force on a Current Loop Torque & Magnetic Dipole

By analogy with electric dipoles, for which:

The expression,

implies that a current loop acts as a magnetic dipole!

Here is the magnetic dipole moment,

and

(Torque on a

current loop)


Dipole moment definition
Dipole Moment Definition

  • Define the magnetic

  • dipole moment of

  • the coil m as:

  • =NiA

    t=m x B

    We can convert this

    to a vector with A

    as defined as being

    normal to the area as

    in the previous slide.



R

L

L

R

L

R

(28 – 15)


Motion of a charged particle in a magnetic field

Motion of a chargedparticle in a magneticField


Trajectory of charged particles in a magnetic field

v

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

Trajectory of Charged Particlesin a Magnetic Field

(B field points into plane of paper.)

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

v

F


Trajectory of charged particles in a magnetic field1

Trajectory of Charged Particlesin a Magnetic Field

(B field pointsinto plane of paper.)

v

B

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

v

F

F

Magnetic Force is a centripetal force


Review of rotational motion

 = s / r  s =  r  ds/dt = d/dt r  v =  r

s

 = angle,  = angular speed,  = angular acceleration

r

at = r  tangential acceleration

ar = v2 / rradial acceleration

The radial acceleration changes the direction of motion,

while the tangential acceleration changes the speed.

at

ar

Uniform Circular Motion

 = constant  v and ar constant but direction changes

ar

KE = ½ mv2 = ½ mw2r2

ar = v2/r = 2 r

v

F = mar = mv2/r = m2r

Review of Rotational Motion


Radius of a charged particle orbit in a magnetic field

Radius of a Charged Particle =  r Orbit in a Magnetic Field

Centripetal Magnetic

Force Force

=

v

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r


Cyclotron frequency

v =  r

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r

Cyclotron Frequency

The time taken to complete one

orbit is:

V cancels !


Mass spectrometer

Smaller Mass =  r

Mass Spectrometer


An example
An Example =  r

A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B  such that


Problem continued

r =  r

Problem Continued


14 chapter 28
#14 Chapter 28 =  r

A metal strip 6.50 cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B= 1.20mTdirected perpendicular to the strip, as shown in the Figure. A potential difference of 3.90 ηV is measured between points x and y across the strip. Calculate the speed v.


  • 21.   =  r (a) Find the frequency of revolution of an electron with an energy of 100 eV in a uniform magnetic field of magnitude 35.0 µT . (b) Calculate the radius of the path of this electron if its velocity is perpendicular to the magnetic field.


  • 39.   =  r A 13.0 g wire of length L = 62.0 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.440 T. What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads?


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