Chapter 29

Electromagnetic Induction and Faraday’s Law

Physics for Scientists & Engineers, 3rd EditionDouglas C. Giancoli

© Prentice Hall

5P20-

Ampere’s Law: .∫ =⋅ encId 0µsB

IB

BLongCircular

Symmetry(Infinite) Current Sheet

XXXXXXXXXXXX

B X XX

X

X

XX

X

XXX

X

X

XX

X

Solenoid =

2 Current Sheets

Torus

6P20-

Group Problem: TorusA torus (a solenoid of radius a and n turns/meter whose ends are bent around to make a donut of radius R) carries a uniform current I.

Find B on what was the central axis of the solenoid

I

I

Ra

7P20-

Ampere’s Law: Torus

Amperian Loop:B is Constant & Parallel

I Penetrates

BXXX

XX

X X XXX

XXXXX

X X XXXR

a

Picture:Solenoid (slinky) curved

around & joined end

to end

10P20-

Magnet Falling Through a Ring

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/faraday/07-FallingMagnetResistive/07-FallMAgRes_f54_320.html

Falling magnet slows as it approaches a copper ring which has been immersed in liquid nitrogen.

12P20-

Jumping Ring

An aluminum ring jumps into the air when the solenoid beneath it is energized

13P20-

What is Going On?

It looks as though the conducting loops have current in them (they behave like magnetic dipoles) even though they aren’t hooked up

Figure 29-1

Figure 29-2 (a)

Figure 29-2 (b)

Figure 29-2 (c)

15P20-

Electromagnetic Induction

19P20-

Faraday’s Law of Induction

BdNdt

ε Φ= −

A changing magnetic flux induces an EMF

Figure 29-3

Figure 29-4

Figure 29-6

Figure 29-5

20P20-

Magnetic Flux Thru Wire LoopAnalogous to Electric Flux (Gauss’ Law)

cosB B A BA θ⊥Φ = = = ⋅B A

BS

d= ⋅∫Φ B A

(1) Uniform B

(2) Non-Uniform B

29P20-

Ways to Induce EMF

( )cosdN BAdt

θε =−Quantities which can vary with time:

• Magnitude of B• Area A enclosed by the loop• Angle θ between B and loop normal

e.g. Falling Magnet

22P20-

Minus Sign? Lenz’s LawInduced EMF is in direction that opposesthe change in flux that caused it

Figure 29-34

Figure 29-31

Figure 29-30

Figure 29-7 (c)

Figure 29-7 (d)

Figure 29-7 (e)

Figure 29-8

30P20-

Group Problem: Changing AreaConducting rod pulled along two conducting rails in a uniform magnetic field B at constant velocity v

1. Direction of induced current?

2. Direction of resultant force?

3. Magnitude of EMF?4. Magnitude of current?5. Power externally

supplied to move at constant v?

Figure 29-9 (a)

Figure 29-9 (b)

31P20-

Ways to Induce EMF

( )cosdN BAdt

θε =−Quantities which can vary with time:

• Magnitude of B• Area A enclosed• Angle θ between B and loop normal

e.g. Moving Coil & Dipole

e.g. Sliding bar

32P20-

Changing Angle

0BΦ = ⋅ =B AB BAΦ = ⋅ =B A

37P20-

DC Motor (magnetostatics)

38P20-

Motors & Generators

cos cosB BA BA tθ ωΦ = =

(cos ) sinBd dN NAB t NAB tdt dt

ω ω ωε Φ= − = − =

Figure 29-21

Figure 29-22 (a)

18P20-

What is EMF?

dε = ⋅∫ E s

Looks like potential. It’s a “driving force” for current

Figure 29-22 (b)

Figure 29-22 (c)

Figure 29-22 (d)