Change Area of loop Change orientation Faraday’s Law of ... · of loop Change orientation Faraday’s Lawof ... flows in a horizontal conducting loop in such a way that the magnetic

Change Area of loop Change orientation

of loop relative to BFaraday’s Law

Notice the minus sign!!!

Putting it Together

AB

dt

d

Electricity & Magnetism Lecture 16, Slide 1

Question


If I attempt to drop a magnet down an iron pipe, it will just stick to the side of the pipe.

What will happened if I attempt to drop a magnet down a copper pipe?

A) It will fall straight through B) It will stick to the side of the pipeC) It will fall very slowly through the pipeD) It will be pulled very fast down the pipe

Physics 2112

Unit 17

Today’s Concept:

Faraday’s Law

Lenz’s Law

dt

ddEemf B


Your Comments

Pretty good lecture.I would really need to discuss the directions of everything defined here. How do you find the direction of the induced emf? of the change in flux? like to discuss how we decide the direction of induced currents.

I feel as though I am going to need a ton of practice with this section. It would be great if you could reiterate the directions and rotations of the induced flux and current.I think I understood this lecture for the most part none Ahhh so so. Please no more integrals. i'm still not caught up! this isn't good! Still confused on this. HOW MANY LAWS ARE THERE IN THIS CLASS! i honestly dont understand. thats too much Faraday is okay but when i see lenz's law in addition,i just skip through all the prelecture. Come on, we're emgineers, not lawyers!! this is all very confusing


The Plan

• Define Magnetic Flux, B

• Introduce Faraday’s Law in terms of magnetic flux

• Do some examples to show how Faraday’s Law explains motional emf results we had last time.


dt

ddEemf B

B

A

Magnetic Flux: AdBB


Define B

Similar to electric flux E

Think of B as the number of field lines passing through the surface

B

A


Example 17.1 (Magnetic Flux)

A copper disk with radius 5cm is placed in a magnetic field of uniform strength 0.2T.

What is the magnetic flux through the disk?

5cm

Notice Units:

AdBB


Units

= T * m2

= N / C /(m/sec) * m2

= (V/m)/(m/sec) * m2

= V*sec

dt

demf B

In Words: • When the flux B through a loop changes, an emf is

induced in the loop.• The emf will make a current flow if it can (like a battery).

• Magnetic fields alone don’t cause currents

• Changing magnetic fields cause currents

Faraday’s Law:

dt

ddEemf B

I


Question

Unit 17, Slide 10

A circular wire loop is placed in a uniform magnetic field pointing to the right. The loop is rotated with constant angular velocity around a vertical axis (dashed line).

At which of the three times shown is the induced emfgreatest?

Unit 17, Slide 11

A circular wire loop is placed in a uniform magnetic field pointing to the right. The loop is rotated with constant angular velocity around a vertical axis (dashed line).

At which of the three times shown is the induced emf greatest?

||||sinsin||||

cos||||

AdBdt

dAdB

dt

d

dABAdBB

Notice Units:

AdBB


Units

= T * m2

= N / C /(m/sec) * m2

= (V/m)/(m/sec) * m2

= V*sec

dt

demf B


Faraday’s Law

dt

AdBdemf

)(

Three ways to change flux

Change |B|Change |A|

Change the angle between the two

A 10cm X 20m loop is formed by a motionless conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W.

The entire apparatus is placed in a magnetic field that varies from 0 to 1.2 T in 30 seconds.

Example 17.2 (Change |B|)

What is the current through the resistor?

B varies

Unit 17, Slide 14

A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W.

The entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen.

Example 17.3 (Change Area)

What is the current through the resistor?

The bar is pulled to the right by a force, F, at a velocity of 8m/sec.

Unit 17, Slide 15

17.4 (Change the angle)

A 10cm X 20 cm loop is rotated at 10rev/sec in a magnetic field of 0.1T.

If the loop is connected to a R = 50W resistor, what is the current?

Unit 17, Slide 16

In words:Whenever the magnetic flux through a

surface changes a current is formed which creates a magnetic field which opposes that change.

dt

ddEemf B

Lenz’s Law

Question


If I attempt to drop a magnet down an iron pipe, it will just stick to the side of the pipe.

What will happened if I attempt to drop a magnet down a copper pipe?

A) It will fall straight through B) It will stick to the side of the pipeC) It will fall very slowly through the pipeD) It will be pulled very fast down the pipe

CheckPoint 1


Suppose a current flows in a horizontal conducting loop in such a way

that the magnetic flux produced by this current points upward.

As viewed from above, in which direction is this current flowing?

CheckPoint 2


A magnet makes the vertical magnetic field shown by the red arrows. A

horizontal conducting loop is entering the field as shown.

At the instant shown below left, what is the direction of the additional flux

produced by the current induced in the loop?

CheckPoint 3


A magnet makes the vertical magnetic field shown by the red arrows. A

horizontal conducting loop is entering the field as shown.

The upward flux through the loop as a function of time is shown by the

blue trace. Which of the red traces below it best represents the current

induced in the loop as a function of time as it passes over the magnet?

(Positive means counter-clockwise as viewed from above):

A point of confusion….

Unit 17, Slide 22

dt

ddEemf B

Induced

Faraday’s Law:

0

dEInduced

Note:

Induced electric field is not conservative!

VldEInduced

Question

Unit 17, Slide 23

A bar magnet is being pushed to the right into a

coil of wire North end first .

According to Lenz’s law, which way will this new

magnetic field point?

A. clockwise

B. up

C. down

D. to the left

E. to the right

Question

Unit 17, Slide 24

A bar magnet is being pushed to the right into a

coil of wire South end first.



A. clockwise

B. up

C. down

D. to the left

E. to the right

Question

Unit 17, Slide 25

A bar magnet is being pulled to the left away

from a coil of wire South end first.



A. clockwise

B. up

C. down

D. to the left

E. to the right

Question

Unit 17, Slide 26

If magnet moves towards a loop in the screen with

the North pole pointed away from the screen. In

what direction is the induced current?

1) clockwise

2) counter-clockwise

3) no induced currentN

Question

Unit 17, Slide 27

If magnet moves towards a loop in the screen with the North pole pointed away from the screen. In what direction is the

induced current?

1) clockwise


3) no induced current

NIncreasing magnetic field

pointing away so you want

a increasing pointing

towards. Clockwise

Question

Unit 17, Slide 28

A wire loop is being pulled through a uniform

magnetic field. What is the direction of the

induced current?

1) clockwise



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







Question

Unit 17, Slide 29

A wire loop is being pulled through a uniform

magnetic field that suddenly ends. What is the

direction of the induced current?

1) clockwise










B

A circular loop of radius R is moving to the right a velocity v in a magnetic field that points to the left. The current in this loop caused by this motion is:

a) clockwiseb) counter-clockwisec) zero

Question


V

(Define “clockwise current” to be current that goes up on the front (left) edge of the loop.)

Question

Unit 17, Slide 31

If a coil is shrinking in a magnetic field

pointing into the page, in what direction

is the induced current?

1) clockwise



Example 17.5 (Bar on Ramp)

Unit 17, Slide 32

A square metal bar has a

length of 1m and a mass

1.2kg and slides down

between two legs of a

conducting U shaped rail that

is at an angle of 45o to the

ground.

45o

The entire rails/rod system has a resistance of 2.5W

and is contained in a vertical 0.7T magnetic field.

What is the maximum velocity of the rod?

. . . .

. . . .

. . . .

Side

view

Top

view

Question

Unit 17, Slide 33

As the bar slides down the

ramp, which way will the

current flow in the bar?45o

A. Into the screen

B. Out of the screen

C. No current will flow in the

bar

. . . .

. . . .

. . . .

Side

view

Top

view

Question

Unit 17, Slide 34

As the bar slides down the

ramp, which way will the

magnetic force on it point?45o

A. Left

B. Right

C. Up

D. Down

E. Into the screen

Side

view

Example 17.6 (solenoid)

Unit 17, Slide 35

A long solenoid has 220

turns/cm and carries a current

I=1.5A. It’s diameter is 3.2cm.

At the center, we place a

closely packed coil, C, with 32

turns that is 2.1cm in diameter.

The current in the solenoid is reduced to zero in 25ms.

What is the magnitude of the EMF induced in the coil while

the current in the solenoid is changing?


Unit 17, Slide 36

A long solenoid has 220 turns/cm

and carries a current I=1.5A. It’s

diameter is 3.2cm. At the center, we

place a closely packed coil, C, with

32 turns that is 2.1cm in diameter.

The current in the solenoid is reduced to zero in 25ms.

I’m going to use Faraday’s law to find the EMF caused by

the changing flux. To find the flux, I’m going to find the

magnetic field over what area?

A) (0.032m)2p B) (0.021m)2p

C) (0.032m/2)2p D) (0.021m/2)2p


Unit 17, Slide 37

Bo = moIn = 0.00414T

o = B*[p*(0.021/2)2]= 1.44X10-5 T m2

d/dt =1.44X10-5/25X10-3 = -5.76X10-4V

= -N d/dt = 32*(5.76X10-4) = 18.4mV

Executive Summary:

emf → current → field a) induced only when flux is changingb) opposes the change

Faraday’s Law:

dt

ddEemf B

where AdBB


Remember?

Unit 15, Slide 39

surface

AdB 0

ENCLo

loop

IldB m

0loop

ldE

o

enc

surface

QAdE

A Change…..

Unit 15, Slide 40

surface

AdB 0

ENCLo

loop

IldB m

dt

dldE B

loop

o

enc

surface

QAdE

Electricity and magnetism are now connected!

Documents

Change Area of loop Change orientation Faraday’s Law of ... · of loop Change orientation Faraday’s Lawof ... flows in a horizontal conducting loop in such a way that the magnetic