phys 2415 no open laptops!!

PHYS 2415

No Open Laptops!!

Professor Stephen Thornton

October 15, 2012

Reading Quiz:Which of the following situations has a changing magnetic flux? B is constant everywhere.The ring is conducting.

A) Only 1

B) Only 2

C) Only 3

D) 1 and 2

E) 1 and 3

swingsrotates up and

down

Reading Quiz: Which of the following situations has a changing magnetic flux? B is constant everywhere.The ring is conducting. Situation 2 is the only one in which the magnetic flux changes. A current will be induced in the ring as a result of the ring rotating in the magnetic field.

A) Only 1B) Only 2C) Only 3D) 1 and 2E) 1 and 3

swingsrotates up and

down

Today

• Changing magnetic fields can produce a

current! Called magnetic induction.

• It is actually change in magnetic flux that

causes induced currents.

• Lots of applications!

• Lenz’s law helps us determine direction of

current.

• Motional emf

• Electric motors and generators depend on it!

Copyright © 2009 Pearson Education, Inc.

Almost 200 years ago, Michael Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

Induced EMF

Do demos about induced currents.

Push and pull magnet in and out of coils of wire to show current production.

Induced Current Produced by a Moving Magnet

v

v


Therefore, a changing magnetic field induces an emf/current.

Faraday’s experiment used a magnetic field that was changing because the current producing it was changing; the previous graphic shows a magnetic field that is changing because the magnet is moving.

Induced EMF

Magnetic Induction

B linked by iron bar.

We conclude that it is the change in magnetic flux that causes induced current.

ind

B B AF =

Faraday’s Discovery and the Law of Induction

There are many ways to change the magnetic flux through a surface:

• Move the magnet

• Turning current on or off in one loop induces current in another

• Move the loop

• Change the shape (and the area) of the loop

The Magnetic Flux Through a Loop

Flux is maximum

Flux is zero. magnetic flux

cosB

B

B A

BA


The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop.

Magnetic flux:

Unit of magnetic flux: weber, Wb:

1 Wb = 1 T·m2.

B B dAF = ò

Look at the mathematics.

This is called Faraday’s Law of Induction after Michael Faraday.

is number of turnsDon't worry about the sign. We willhave a better way to find this later.

Induced emf BdN

dt

N

Do some more demos.

1) Magnet through coil again.2) Flash bulb3) LED coil

Lenz’s Law

The induced current will always be in the direction to oppose the change that produced it.

Induced emf Induced currentÛ

Applying Lenz’s Law to a Magnet Moving Toward and Away From a Current Loop

v v

Induced current

Conceptual Quiz:A long, straight wire carries a steady current I. A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop is

A) clockwise.B) counterclockwiseC) need more information

Answer: BThe loop has an increasing flux into the screen. A current will be induced to create a magnetic field coming out of the screen. The current will be counterclockwise to do this.

Iind

Lenz’s Law Applied to a Decreasing Magnetic Field

Changing area. What happens to magnetic flux?What is direction of induced current?


Problem Solving: Lenz’s Law

1. Determine whether the magnetic flux is increasing, decreasing, or unchanged.

2. The magnetic field due to the induced current points in the opposite direction to the original field if the flux is increasing; in the same direction if it is decreasing; and is zero if the flux is not changing.

3. Use the right-hand rule to determine the direction of the induced current.

4. Remember that the external magnetic field and the magnetic field due to the induced current are different.

Faraday’s Law of Induction; Lenz’s Law

If a North pole moves If a North pole moves toward the loop from above toward the loop from above the page, in what direction is the page, in what direction is the induced current? the induced current?

A) clockwiseA) clockwise

B) counterclockwiseB) counterclockwise

C) no induced currentC) no induced current

Conceptual Quiz

If a North pole moves toward If a North pole moves toward the loop from above the page, the loop from above the page, in what direction is the in what direction is the induced current? induced current?




The magnetic field of the moving bar

magnet is pointing into the pageinto the page and

getting largerlarger as the magnet moves

closer to the loop. Thus the induced

magnetic field has to point out of the out of the

pagepage. A counterclockwisecounterclockwise induced

current will give just such an induced

magnetic field.

Conceptual Quiz

Follow-up:Follow-up: What happens if the magnet is stationary but the loop moves? What happens if the magnet is stationary but the loop moves?




If a coil is shrinking in If a coil is shrinking in a magnetic field a magnetic field pointing into the page, pointing into the page, in what direction is the in what direction is the induced current? induced current?

Conceptual Quiz

The magnetic flux through the loop is

decreasingdecreasing, so the induced B field must

try to reinforce it and therefore points in

the same direction — into the pageinto the page.

According to the right-hand rule, an

induced clockwiseclockwise current will generate

a magnetic field into the pageinto the page.




If a coil is shrinking in If a coil is shrinking in a magnetic field a magnetic field pointing into the page, pointing into the page, in what direction is the in what direction is the induced current? induced current?

Conceptual Quiz

Follow-up:Follow-up: What if the What if the B B field is oriented at 90° to its present direction?field is oriented at 90° to its present direction?

Motional emf

What happens when we push rod down?

Determining the Direction of an Induced Current

We exert force to push bar down.

Force and Induced Current

ind

Bd dA vdtB B B v

dt dt dtB v

IR R

Induced current to oppose change

A different situation. Rod goes out.

Ä

Ä

Ä

Motional emf• Created by a conductor moving in

a magnetic field

• “Loop” is imaginary but real emf is induced in conductor

Find force and energy2 2

2 2 2

mechanical

2 2 2 22

electrical

B vF B B

R

B vP Fv

R

Bv B vP I R R

R

BI

R

R

v

They are equal!

If a coil is rotated as shown, If a coil is rotated as shown,

in a magnetic field pointing in a magnetic field pointing

to the left, in what direction to the left, in what direction

is the induced current? is the induced current?




Conceptual QuizConceptual Quiz

As the coil is rotated into the B field,

the magnetic flux through it increasesincreases.

According to Lenz’s law, the induced B

field has to oppose this increaseoppose this increase, thus

the new B field points to the rightto the right. An

induced counterclockwisecounterclockwise current

produces just such a B field.

If a coil is rotated as shown, If a coil is rotated as shown,

in a magnetic field pointing in a magnetic field pointing

to the left, in what direction to the left, in what direction

is the induced current? is the induced current?





A wire loop is being pulled away A wire loop is being pulled away

from a current-carrying wire. from a current-carrying wire.

What is the direction of the What is the direction of the

induced current in the loop?induced current in the loop?

I





The magnetic flux is into the pageinto the page on the

right side of the wire and decreasingdecreasing due

to the fact that the loop is being pulled

away. By Lenz’s law, the induced B field

will oppose this decreaseoppose this decrease. Thus, the new

B field points into the page,into the page, which

requires an induced clockwiseclockwise current to

produce such a B field. I





A wire loop is being pulled away A wire loop is being pulled away

from a current-carrying wire. from a current-carrying wire.

What is the direction of the What is the direction of the

induced current in the loop?induced current in the loop?

What is the induced current if What is the induced current if

the wire loop moves in the the wire loop moves in the

direction of the direction of the yellow arrowyellow arrow??




I


The magnetic flux through the loop magnetic flux through the loop

is not changingis not changing as it moves parallel

to the wire. Therefore, there is no no

induced currentinduced current.

I




What is the induced current if What is the induced current if

the wire loop moves in the the wire loop moves in the

direction of the direction of the yellow arrowyellow arrow??


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







A wire loop is being A wire loop is being pulled through a pulled through a uniform magnetic field. uniform magnetic field. What is the direction of What is the direction of the induced current? the induced current?




Conceputal Quiz

Since the magnetic field is uniform, the

magnetic flux through the loop is not magnetic flux through the loop is not

changingchanging. Thus no current is inducedno current is induced.








A wire loop is being A wire loop is being pulled through a pulled through a uniform magnetic field. uniform magnetic field. What is the direction of What is the direction of the induced current? the induced current?




Conceptual Quiz

Follow-up:Follow-up: What happens if the loop moves out of the page? What happens if the loop moves out of the page?




A wire loop is being A wire loop is being pulled through a pulled through a uniform magnetic field uniform magnetic field that suddenly endsthat suddenly ends. . What is the direction of What is the direction of the induced current? the induced current?

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

Conceptual Quiz




A wire loop is being A wire loop is being pulled through a pulled through a uniform magnetic field uniform magnetic field that suddenly endsthat suddenly ends. . What is the direction of What is the direction of the induced current? the induced current?

The BB field into the page field into the page is disappearing in

the loop, so it must be compensated by an

induced flux also into the pageinduced flux also into the page. This can

be accomplished by an induced current in induced current in

the clockwisethe clockwise directiondirection in the wire loop.

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

Conceptual Quiz

Follow-up:Follow-up: What happens when the loop is completely out of the field? What happens when the loop is completely out of the field?

A conducting rod slides on a

conducting track in a constant

B field directed into the page.

What is the direction of the

induced current?

x x x x x x x x x x x




v





A conducting rod slides on a

conducting track in a constant

B field directed into the page.

What is the direction of the

induced current?





v

The B field points into the pageinto the page. The flux is increasingincreasing since the area is increasing. The induced B field opposes this change and therefore points out of the pageout of the page. Thus, the induced current runs counterclockwise,counterclockwise, according to the right-hand rule.





Follow-up:Follow-up: What direction is the magnetic force on the rod as it moves? What direction is the magnetic force on the rod as it moves?

phys 2415 no open laptops!!

Documents

changing magnetic flux

changing magnetic field

direction of induced

unit of magnetic flux

loopthe magnetic flux

magnetic flux changes

direction of current

magnetic fields