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## PowerPoint Slideshow about ' Magnetic field' - kenyon-bray

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### Magnetic field

### Motion of a chargedparticle in a magneticField

### Trajectory of Charged Particlesin a Magnetic Field

### Trajectory of Charged Particlesin a Magnetic Field

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

### Cyclotron Frequency

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

- 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 PhysicsThere 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 Wire in More Detail

Assume all electrons are moving

with the same velocity vd.

L

B out of plane of the paper

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 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

- 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.

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

(B field points into plane of paper.)

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

v

F

(B field pointsinto plane of paper.)

v

B

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

v

F

F

Magnetic Force is a centripetal force

= 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 = m2r

Review of Rotational MotionCentripetal Magnetic

Force Force

=

v

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r

v = r

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r

The time taken to complete one

orbit is:

V cancels !

Smaller Mass = r

Mass SpectrometerAn 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

r = r

Problem Continued#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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