Physics 102: Lecture 10, Slide 1

Faraday’s Law

Physics 102: Lecture 10

Changing Magnetic Fields create Electric Fields

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

Motional EMF

V

• A metal bar slides with velocity v on a track in a uniform B field

• Moving + charges in bar experience force down (RHR1)

• Electrical current driven clockwise!

• Moving bar acts like a battery (i.e. generates EMF)!!

Fq

(Recall that e- actually move, opposite current)

+qI

Physics 102: Lecture 10, Slide 4

Faraday’s Law of Induction:

“induced EMF” = rate of change of magnetic flux

𝜀= −∆ΦΔ𝑡 = −Φf −Φi𝑡𝑓 − 𝑡𝑖

• The principle that unifies electricity and magnetism• Key to many things in E&M

– Generating electricity– Microphones, speakers, guitar pickups– Amplifiers– Computer disks and card readers

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.

A Magnetic flux = B A(Units Tm2 = Wb)

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 A cos(0) = BAB = B A cos(90) = 0

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

Physics 102: Lecture 10, Slide 7

Faraday’s Law of Induction:

“induced EMF” = rate of change of magnetic flux

Since = B A cos(), 3 things can change

1. Area of loop

2. Magnetic field B

3. Angle between normal and B

𝜀= −∆ΦΔ𝑡 = −Φf −Φi𝑡𝑓 − 𝑡𝑖

Physics 102: Lecture 10, Slide 8

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 9

Faraday: Change Area

V

t=00=BLW

tt=BL(W+vt)

L

W

V

W vt

EMF Magnitude:

= B A cos()

ȁ 𝜀ȁ = ∆ΦΔ𝑡 = Φf − Φi𝑡− 0 = 𝐵𝐿(𝑤+ 𝑣𝑡) − 𝐵𝐿𝑤𝑡− 0 = 𝐵𝐿𝑣

What about the sign of the EMF?

Physics 102: Lecture 10, Slide 10

Lenz’s Law (EMF direction)

V V

• Flux is increasing• Induced current is clockwise• Current loop generates induced B field

– from RHR2, into page, opposite external B field!

IBind

What happens if the velocity is reversed?

Physics 102: Lecture 10, Slide 11

Lenz’s Law (EMF direction)

VV

• Flux is decreasing• Induced current is counterclockwise• Current loop generates induced B field

– from RHR2, out of the page, along external B field!

I

Induced EMF opposes change in flux

Bind

Physics 102: Lecture 10, Slide 12

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

𝜀= −∆ΦΔ𝑡 = −Φf − Φi𝑡𝑓 − 𝑡𝑖

Physics 102: Lecture 10, Slide 13

Motional EMF circuit

• Direction of Current

• B field generates force on current-carrying bar

I = /R

• Magnitude of current

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

Fbar = ILB sin(), to left (RHR1)

V

Fbar opposes v!

= vBL/R

I

Fq

+q

Fbar

• Careful! There are two forces:Fbar = force on bar from induced currentFq = force on + charges in bar driving induced current

Physics 102: Lecture 10, Slide 14

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

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

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

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

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

Motional EMF circuit

I = /R = vBL/R

Still to left, opposite v

What happens if field is reversed? (TRY IT AT HOME)

V

• 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)

F always opposes v, bar slows down Must apply external force to keep bar moving

Physics 102: Lecture 10, Slide 15

Preflight 10.4

• Increase• Stay the Same• Decrease

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

F=ILB sin()

Physics 102: Lecture 10, Slide 17

Faraday’s Law of Induction:

“induced EMF” = rate of change of magnetic flux

Since = B A cos(), 3 things can change

1. Area of loop

2. Magnetic field B

3. Angle between normal and B

𝜀= −∆ΦΔ𝑡 = −Φf −Φi𝑡𝑓 − 𝑡𝑖

Physics 102: Lecture 10, Slide 18

ACT: Induction cannon (Demo)

As current increases in the solenoid, what direction will induced current be in ring?

1) Same as solenoid

2) Opposite of solenoid

3) No current

Bsol

A solenoid is driven by an increasing current. A loop of wire is placed around it

Physics 102: Lecture 10, Slide 19

Induction cannon (Demo)

• Recall: current loop behaves like bar magnet

• Opposite currents => opposite polarities

• Like poles repel! Loop shoots up

A solenoid is driven by an increasing current. A loop of wire is placed around it

• What happens when loop has less resistance?

• What happens if the loop is broken?

Physics 102: Lecture 10, Slide 20

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

1) Up

2) Down

ACT: Change B (Demo)

Demo 371

Physics 102: Lecture 10, Slide 21

ACT: Change B II (cont’d)

If I reduce the resistance in the wire, the magnet will fall

1) faster

2) slower

3) at the same speed N

S

Physics 102: Lecture 10, Slide 24

Faraday’s and Lenz’s Law

Faraday: Induced emf = rate of change of magnetic flux

Since = B A cos(), 3 things can change

1. Area of loop

2. Magnetic field B

3. Angle between normal and B

𝜀= −∆ΦΔ𝑡 = −Φf −Φi𝑡𝑓 − 𝑡𝑖

Next lecture

Lenz: Induced emf opposes change in flux