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Electromagnetism

Electromagnetism Canada’s Triumph Accelerator

Putting it All Together

Hydrogen Minus

Initial Acceleration

Electrostatic

Circular Motion

Magnetic Steering

Filtering

Electromagnetism Review

Magnetic Flux

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 Faraday’s Law.


cosB BA

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

Magnetic Flux

Magnetic Field(Tesla)

Area of Surface(m2)

Angle between field and normal line (B) on

the Surface Area

This can be described by the equation

Magnetic Flux

Electromagnetism Review Magnetic Flux Observations

The Stronger the Magnetic Field (B), the greater the Flux ().

The larger the Area (A), the greater the Flux ().

If the Magnetic Field (B) is perpendicular to the area, then the Flux () will be at a maximum.

cosB BA

Electromagnetism Review Magnetic Flux Units

Since B = BAcos(θ)

Flux has the units of B x A

This is (Tesla)(Metre2)

This is also called a Weber (Wb)

Electromagnetism Review Magnetic Flux Units

When the field is perpendicular to the plane of the loop

θ = 0 and ΦB = ΦB, max = BA

When the field is parallel to the plane of the loop.

θ = 90° and ΦB = 0The flux can be negative, for

example if θ = 180°

When the field is at an angle θ to the field B, ΦB is less than max.

Electromagnetism Review Magnetic Flux by Larger Area

You can increase the magnetic Flux by increasing the Surface Area

Electromagnetism Review Magnetic Flux by Strengthening the Field

You can increase the magnetic Flux by Strengthening the Field.

Electromagnetism Review Magnetic Flux Practice Question

cosB BA

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 200 away from the Earth’s North pole. What is the flux through the hoop?

cosB BA

5 25 10 0 cos.5 20B T m

2 cosB rB

53.7 10B Wb


Induction

Faraday’s Law describes the relationship between Electric Current and Magnetism.

Faraday’s Law

An Electric Current can induce a Magnetic Field, and a Magnetic Field can induce a Electric Current.

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 .


Law of Induction

Induced Voltage, V. A voltage is generated a Magnetic Force has been traditionally called an Electromotive Force or emf.

Faraday’s Law

Nt

Change in Magnetic Flux, Wb

Change in time, sThe number of coils of wire

•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.

Electromagnetism Review Faraday’s Law Practice Question

Nt

You have a coil of wire with 30 loops, each of which has an area of 2.0 x 10-3 m2. 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.

Nt

3 21.1 1.0 2.0 10 cos 030

0.2 0.0

T T m

s s

cosBAN

t

0.03V

cosB BA


B Direction

Lenz’s Law describes the direction of the Electric Current produced by a changing Magnetic Field.

Lenz’s Law

The Thumb points in the direction of the Current. The fingers curl in the direction of the Magnetic Field.


B Direction

An influenced emf gives rise to a Electric Current whose Magnetic Field opposes the original change in Flux.

Lenz’s Law

The Right Hand Rule can aid us in these situations.

Electromagnetism Review Lenz’s Law

X X X X X X XX X X X X X XX X X X X X XX X X X X X XX X X X X X XX X X X X X XX 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.

Change in Flux

The induced current attempts to maintain the status quo.


Hoop Entering B Field


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.



Hoop Inside B Field


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.


Hoop Exiting B Field


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.



Magnet Moving Through Hoop

When a magnet passes through a closed loop, the current will flow in what directions?

When a magnet enters the loop the current will flow clockwise (to oppose the increase in flux, make the end of the loop the magnet enters 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).

NS

When the North end of a magnet enters the loop from behind the screen, which direction, if any, will the current flow in the wire?


Magnet Moving Through Hoop

The current will flow clockwise to oppose the increasing flux.


EMF induced in a Moving Conductor

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.

EMF


EMF in a Moving Conductor

Induced Electromotive Force or emf.

Faraday’s Law

BLv

Velocity in m/s.

Length of moving conductor in m.

Magnetic Field in T.



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.

EMF

X X X X X X X X X X XX X X X X X X X X X XX X X X X X X X X X XX X X X X X X X X X XX X X X X X X X X X X



EMF


BLv

1.2 2.0 7

17

mT m

s

V

+ vq

• Force on 1 moving charge:F = q v B sin(q)Out of the page (RHR)

• Force on many moving charges:F = (q/t)(vt)B sin(q)

= I L B sin(q) Out of the page!

v

L = vt

B

I = q/t+ + ++

distance


Force of Magnetic Field on Current

Recall

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

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

(length x width = area) LW = A

Torque is t = I A B sin(f)

W

L

a b

cd

B

I

XF

•F

Torque on Current Loop in B field

a b

cd

F

F

f

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

Understanding: Torque on Current Loop

What is the torque on the loop below?

1) t < IAB

2) t = IAB

3) t > IAB

t = 0

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:

t = I A B sinf.

(area of loop)

Magnitude:

t = I A B sinf

Direction:

N

# of loops

a

b

c

dB

normal

f

F

F

Torque on Current Loop

between normal and B

B

Compare the torque on loop 1 and 2 which have identical area, and current.

I

Understanding: Torque

(1)

B

I

(2)

1) t1 > t2 2) t1 = t2 3) t1 < t2

Area points out of page for both!

f = 90 degrees

t = I A B sinf

Motional EMF

F = q v B sin(q)+ v

+-

-

+

Potential Difference F d/q

EMF = q v B sin(q) L/q

= v B L

B

L v

Velocity

Velocity

Moving + charge feels force downwards:

Moving + charge still feels force downwards: B

F

Angle between v and B

Understanding

Which bar has the larger motional emf? a b

v

v

ε = v B L sin(q)

q is angle between v and B

Case a: q = 0, so ε = 0

Case b: q = 90, so ε = v B L

“a is parallel, b is perpendicular”

Motional EMF circuit

Direction of Current

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

I = e/R

• Magnitude of current

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

To left, slows down

Moving bar acts like battery e = vBL

B

-+

V

What changes if B points into page?

= vBL/R

Motional EMF circuit

I = e/R = vBL/R

Still to left, slows down

Moving bar acts like battery e = vBL B

+ -

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

Direction of Current

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

• Magnitude of current

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

Understanding

IncreaseStay the SameDecrease

Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.

To keep the bar moving at the same speed, the force supplied by the hand will have to:

F=ILB sin(q))

B and v still perpendicular (q=90), so F=ILB just like before!


Fm

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Fm

Understanding

True False

Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.

To keep the bar moving to the right, the hand will have to supply a force in the opposite direction.

Current flows in the opposite direction, so force direction from the B field remains the same!

BLv

BLvI

R


Fm

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Fm

Applications of Magnetic Force

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.

Examples of Induced Current

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

Induced Current

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.

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

circuit. AC currents must be used.

75,000 V in the power lines

120 V in your house

s

p

s

p

p

s

N

N

V

V

I

I

p = primary

s = secondary

GeneratorA coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil.

Applets

Wires:

Flux area:

Electric/Magnetic Balance:

Flux:

Induced Current:

Moving Bar:

Generator:

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