Physics 102: Lecture 10, Slide 1

Faraday’s LawPhysics 102: Lecture 10

Changing Magnetic Fields create Electric Fields

Last Two Lectures

• Magnetic fields

• Forces on moving charges and currents

• Torques on current loops

• Magnetic field due to– Long straight wire– Solenoid

Physics 102: Lecture 10, Slide 2

Last Two Lectures

• Magnetic fields

• Forces on moving charges and currents

• Torques on current loops

• Magnetic field due to– Long straight wire– Solenoid

Physics 102: Lecture 10, Slide 3

Today: Faraday’s Law

• The principle that unifies electricity and magnetism

• Key to many things in E&M– Generating electricity– Microphones, speakers and tape decks– Amplifiers– Computer disks and card readers

Physics 102: Lecture 10, Slide 4

Physics 102: Lecture 10, Slide 5

First a preliminary: Magnetic Flux

• “Counts” number of field lines through loop.

Uniform magnetic field, B, passes through a plane surface of area A.AMagnetic flux = B A

Magnetic flux B A cos() is angle between normal and B

B

A

normal

B

Note: The flux can be negative(if field lines go thru loop in opposite direction)

Physics 102: Lecture 10, Slide 6

Preflight 10.7

Compare the flux through loops a and b.

1) a>b 2) a< b

ab

nn B

A =

B =

“more lines pass through its surface in that position.”

Physics 102: Lecture 10, Slide 7

Faraday’s Law of Induction:This is new physics and not simply an application of stuff you already know

“induced emf” = rate of change of magnetic flux

if

if

ttt

Since = B A cos(3 things can change

1. Area of loop

2. Magnetic field B

3. Angle between A and B

Physics 102: Lecture 10, Slide 8

Physics 102: Lecture 10, Slide 9

Lenz’s Law (EMF Direction)

Induced emf opposes change in flux

EMF does NOT oppose B field, or flux!

EMF opposes the CHANGE in flux

• If flux increases: New EMF makes new field opposite to original

field

• If flux decreases:New EMF makes new field in same direction

as original field

Physics 102: Lecture 10, Slide 10

ACT: Change Area

1v

v

3

Which loop has the greatest induced EMF at the instant shown above?

L

W

2

v

Physics 102: Lecture 10, Slide 11

Example: Change Area

V

t=00=BLW

tt=BL(W+vt)

t

BLWvtWBL

ttt

)(

00 vBL

L

W

V

W vt

EMF Direction: B is out of page and is increasing so EMF creates B field (inside loop) going into page.

I

EMF Magnitude:

= B A cos()

Physics 102: Lecture 10, Slide 12

Physics 102: Lecture 10, Slide 13

Motional EMF circuit

• Direction of Current

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

I = /R

• Magnitude of current

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

To left, slows down

Moving bar acts like battery = vBL

B

-+

V

What changes if B points into page?

= vBL/R

Physics 102: Lecture 10, Slide 14

Motional EMF circuit

I = /R = vBL/R

Still to left, slows down

Moving bar acts like battery = 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()) on bar due to magnetic field

• Magnitude of current

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

18

Physics 102: Lecture 10, Slide 15

Preflight 10.4

• Increase• Stay the Same• Decrease

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:

19

Physics 102: Lecture 10, Slide 16

Physics 102: Lecture 10, Slide 17

Preflight 10.5

• 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.

Physics 102: Lecture 10, Slide 18

ACT: Change BAs current is increasing in the

solenoid, what direction will current be induced in ring?

1) Same as solenoid

2) Opposite of solenoid

3) No current

SN

Physics 102: Lecture 10, Slide 19

ACT: Change B II

S

N

N

S

Which way is the magnet moving if it is inducing a current in the loop as shown?

1) Up

2) Down

Physics 102: Lecture 10, Slide 20

Physics 102: Lecture 10, Slide 22

Change A flat coil of wire has A=0.2 m2 and R=10. At time t=0, it is

oriented so the normal makes an angle 0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF.

n

B

A

if

if

ttt

i = B A cos(0)

f = B A cos(30)

= 6.43x10-3 Volts

What direction is the current induced?

5.0))0cos()30(cos( BA

Physics 102: Lecture 10, Slide 23

Magnetic Flux ExamplesA conducting loop is inside a solenoid (B=onI). What happens to the flux through the loop when you…

Increase area of solenoid?

Increase area of loop?

Increase current in solenoid?

Rotate loop slightly? B A cos()

Physics 102: Lecture 10, Slide 24

Physics 102: Lecture 10, Slide 25

Magnetic Flux II

Increase area of solenoid

Increase area of loop

Increase current in solenoid

A solenoid (B=onI) is inside a conducting loop. What happens to the flux through the loop when you…

B A cos()

Physics 102: Lecture 10, Slide 26

Motional EMF, Preflight 10.1

F = q v B sin()+ v

+-

-

+

Potential Difference = F L/q

EMF = q v B sin() L/q

=

B

L v

Velocity

Moving + charge feels force downwards:

Moving + charge still feels force downwards: B

F

Physics 102: Lecture 10, Slide 27

Preflight 10.2

• Which bar has the larger motional emf? a b

v

v

E = v B L sin()

is angle between v and B

Case a: = 0, so E = 0

Case b: = 90, so E = v B L

Physics 102: Lecture 10, Slide 28