03/12/2010

Putting it All Together

Hydrogen Minus

Electromagnetism

Initial Acceleration

Electrostatic

Circular Motion

Magnetic Steering

Filtering

Electromagnetism Review

Electromagnetism Review

Magnetic Flux

Magnetic Flux

Flux can be described as the total number of lines passing though an area, loop or coil.

We can describe the Density (or

amount) of a Magnetic Field with the

concept of Magnetic Flux.

Flux can be described as the total

number of lines passing though an

area, loop or coil.

It is a quantity of convenience used in

Magnetic Flux

B BAcos

Magnetic Field

(Tesla)

Angle between field

and normal line (B)

on the Surface Area

Area of Surface

(m 2 )

This can be

described by

the equation

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03/12/2010

Electromagnetism Review

B BAcos

Magnetic Flux Observations

Electromagnetism Review

Magnetic Flux Units

The Stronger the Magnetic Field (B),

the greater the Flux ().

Since

B = BAcos(θ)

Flux has the

units of B x A

The larger the Area (A), the greater

the Flux ().

This is also called

a Weber (Wb)

This is

(Tesla)(Metre 2 )

If the Magnetic Field (B) is

perpendicular to the area, then the

Flux () will be at a maximum.

Electromagnetism Review

Magnetic Flux Units

Electromagnetism Review

Magnetic Flux by Larger Area

When the field is perpendicular

to the plane of the loop

θ = 0 and Φ B = Φ B, max = BA

When the field is parallel to the

plane of the loop.

θ = 90° and Φ B = 0

The flux can be negative, for

example if θ = 180°

When the field is at an angle θ to

the field B, Φ B is less than

max.

You can increase the

magnetic Flux by

increasing the

Surface Area

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03/12/2010

Electromagnetism Review

Magnetic Flux by Strengthening the Field

Electromagnetism Review

Magnetic Flux Practice Question

B BAcos

You have a hula loop of radius 0.5m that is immersed

in the Earth’s magnetic field (5x10 -5 T). The hula loop

is oriented in such a way that the normal is tilted at an

angle of 20 0 away from the Earth’s North pole. What is

the flux through the hoop?

B BAcos

B

B r 2 cos

You can increase the

magnetic Flux by

Strengthening the Field.

.5 20

B 5 10 T 0 m cos

5

3.710

Wb

B

5 2

Electromagnetism Review

Electromagnetism Review

Induction

Law of Induction

relationship between Electric Current

and Magnetism.

An Electric Current can induce a

Magnetic Field, and a Magnetic Field

can induce a Electric Current.

Induced Voltage, V.

A voltage is generated a Magnetic

an Electromotive Force or emf.

The number of coils

of wire

N

t

Change in Magnetic

Flux, Wb

Change in time, s

Just as Electricity needs to be moving

to create a Magnetic field B, The

Magnetic field B needs to be moving

to create an Electric Current .

The greater the change in Magnetic Flux in a wire loop, the

greater the Induced Current.

•Less time corresponds to a greater Induced Current.

•Adding more loops corresponds to a greater Induced Current.

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03/12/2010

Electromagnetism Review

N

t

Electromagnetism Review

B Direction

Lenz’s Law

You have a coil of wire with 30 loops, each of which has

an area of 2.0 x 10 -3 m 2 . The Magnetic Field B is

perpendicular to the surface. At time t=0 s, the Field B is

measured at 1.0 T. At time, t=.2 s, the Field B is measured

at 1.1 T. What is the average emf inside the coils.

Lenz’s Law describes the direction of

the Electric Current produced by a

changing Magnetic Field.

N

t

BAcos

N

t

0.03V

B BAcos

1.1 1.0 2.0 10 3 2

T T m cos 0

30

0.2s

0.0s

The Thumb points in the direction of

the Current. The fingers curl in the

direction of the Magnetic Field.

Electromagnetism Review

Lenz’s Law

Electromagnetism Review

Lenz’s Law

B Direction

Change in Flux

An influenced emf gives rise to a

Electric Current whose Magnetic Field

opposes the original change in Flux.

The Right Hand Rule can aid us in

these situations.

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

Notice how the area is lessened when the loop is stretched.

Since the Flux is reduced, the Electric Current flows in the

direction that would produce the B field. This direction tries

to help maintain the original Flux.

The induced current attempts to maintain the status quo.

4

N

S

03/12/2010

Electromagnetism Review

Lenz’s Law

Electromagnetism Review

Lenz’s Law

Hoop Entering B Field

Hoop Inside B Field

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

When the loop enters a Magnetic

Field. An Electric Current is induced

(counter clockwise) in the loop as to

oppose the increase in the Flux inside

the loop.

When the loop is total immersed

inside a Magnetic Field there is No

increase in Flux therefore there is No

Current flow in the loop.

Electromagnetism Review

Lenz’s Law

Electromagnetism Review

Lenz’s Law

Hoop Exiting B Field

Magnet Moving Through Hoop

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

X X X X X X X

When the loop exits a Magnetic Field.

An Electric Current is induced

(clockwise) in the loop as to oppose

the decrease in the Flux inside the

loop.

When a magnet enters the

loop passes the through current will flow

clockwise a closed loop, (to oppose the

increase the current in flux, will make the

end flow of in the what loop the magnet

enters directions? act like a North

Pole) then zero. As the

magnet exits, the current

will then flow counter

clockwise (to oppose the

decrease in flux, ie look

like a South Pole).

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03/12/2010

Electromagnetism Review

Lenz’s Law

Electromagnetism Review

EMF

Magnet Moving Through Hoop

EMF induced in a Moving

Conductor

When the North end of a

The magnet current enters will the flow loop clockwise from

to behind oppose the the screen, increasing which flux.

direction, if any, will the

current flow in the wire?

We have a conducting bar moving across

a U shaped wire. The magnetic field is

coming out of the screen. As the bar

moves across the wire, the amount of Flux

inside the loop increases.

Electromagnetism Review

Electromagnetism Review

EMF

EMF in a Moving Conductor

EMF induced in a Moving Conductor

Induced Electromotive Force or emf.

Velocity in m/s.

A 2.0 m rod is moving at 7 m/s perpendicular

to a 1.2 T magnetic field heading into the

screen. Determine the induced emf.

BLv

Magnetic Field in T.

Length of moving

conductor in m.

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

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03/12/2010

Electromagnetism Review

EMF

Electromagnetism Review

Recall

EMF induced in a Moving Conductor

Force of Magnetic Field on Current

BLv

m

1.2T 2.0m7

s

17V

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

X X X X X X X X X X X

• Force on 1 moving charge:

‣ F = q v B sin()

‣ Out of the page (RHR)

• Force on many moving charges:

‣ F = (q/t)(vt)B sin()

= I L B sin()

+

‣Out of the page!

+

v

+ + +

v

L = vt

B

I = q/t

distance

Torque on Current Loop in B field

W

d

a

• F

L

Force on sections B-C and A-D: F = IBW

Torque on loop is t = L F sin(f) = ILWB sin(f)

Torque is

I

(length x width = area)

c

F

X

b

B

t = I A B sin(f)

LW = A

F

d

f

a

b

c

F

Understanding: Torque on

Current Loop

What is the torque on the loop below?

1

2

3

t < IAB

t = IAB

t > IAB

t = 0

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x

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03/12/2010

Torque on Current Loop

Understanding: Torque

Magnitude:

t = I A B sinf

F

f

B

B

B

Direction:

Torque tries to line up the normal with B!

(when normal lines up with B, f=0, so t=0! )

Even if the loop is not rectangular, as long as it is flat:

# of

loops

between normal and B

t = N I A B sinf.

(area of

loop)

F

I

(1)

Compare the torque on loop 1 and 2 which have

identical area, and current.

Area points out

of page for both!

1) t 1 > t 2 2) t 1 = t 2 3) t 1 < t 2

t = I A B sinf

(2)

f = 90 degrees

B

B

-

+

+ v

F

L

-

+

Motional EMF

Moving + charge feels force downwards:

v

F = q v B sin()

Velocity

Moving + charge still feels force downwards:

Potential Difference F d/q

EMF = q v B sin() L/q

= v B L

Angle between

v and B

Understanding

• Which bar has the

larger motional emf? a b

ε = v B L sin()

is angle between v and B

Case a: = 0, so ε = 0

Case b: = 90, so ε = v B L

v

“a is parallel, b is perpendicular”

v

Velocity

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03/12/2010

Motional EMF circuit

Moving bar acts like battery = vBL

• Magnitude of current

I = /R = vBL/R

• Direction of Current

Clockwise (+ charges go down thru bar, up thru bulb)

• Direction of force (F=ILB sin()) on bar due to

magnetic field

What changes if B

points into page?

To left, slows down

B

-

+

V

Motional EMF circuit

Moving bar acts like battery = vBL

• Magnitude of current

I = /R = vBL/R

• Direction of Current

Still to left, slows down

B

x x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x x

V

+

x x x x x x x x x x x x x x x x x

-

x x x x x x x x x x x x x x x x x

x x x x x x x x x x x x x x x x x

Counter-Clockwise (+ charges go up thru bar, down thru bulb)

• Direction of force (F=ILB sin()) on bar due to

magnetic field

Understanding

Suppose the magnetic

field is reversed so that it

now points OUT of the

shown in the figure.

X o X o o X o X o X o v X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o

F

X

m

X o X o o X o X o X o X o X o X o X o o X o X

To keep the bar moving at the same speed, the force

supplied by the hand will have to:

• Increase

• Stay the Same F=ILB sin())

• Decrease

B and v still perpendicular (=90), so F=ILB just

like before!

Understanding

Suppose the magnetic

field is reversed so that

it now points OUT of the

shown in the figure.

X o X o o X o X o X o v X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o X

X o X o o X o X o X o X o X o X o X o o X o

F

X

m

X o X o o X o X o X o X o X o X o X o o X o X

To keep the bar moving to the right, the hand will

have to supply a force in the opposite direction.

• True

BLv

BLv

• False

I

R

Current flows in the opposite direction, so force

direction from the B field remains the same!

9

03/12/2010

Applications of Magnetic Force

Examples of Induced Current

Any change of current in primary induces a current in secondary.

Electric currents (in a wire, in a plasma, in a fluid solution, inside an

atom) produce a disturbance in the surrounding space called the

magnetic field. This magnetic field produces forces on any other

macroscopic or microscopic currents.

Example: MRI: Magnetic field (several Tesla) from superconducting

solenoid induces a net alignment of the microscopic currents inside

each and every proton at the center of the Hydrogen atoms in your

body.

Induced Current

Transformers

A transformer is a device used to change the voltage in a

circuit. AC currents must be used.

The current in the primary polarizes the material of the core.

The magnetic field of the primary solenoid is enhanced by the

magnetic field produced by these atomic currents.

• This magnetic field remains confined in the iron core, and only fans

out and loops back at the end of the core.

• Any change in the current in the primary (opening or closing

switch) produces a change in the magnetic flux through the

secondary coil. This induces a current in the secondary.

75,000 V in the

power lines

I Vp

N

s

p

I p Vs

Ns

p = primary

s = secondary

10

03/12/2010

Generator

A coil of wire turns

in a magnetic field.

The flux in the coil

is constantly

changing,

generating an emf

in the coil.

Wires:

Flux area:

Electric/Magnetic Balance:

Applets

Flux:

Induced Current:

Moving Bar:

Generator:

11

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