PHY2049: Chapter 30 2

Chapter 30: Electromagnetic Induction

PHY2049: Chapter 30 3

Subjects

Induced emfFaraday’s law (law #3 of electricity and magnetism)Lenz’s lawMotional emf

Inductance

RL circuits

Magnetic energy

Generators, transformers

PHY2049: Chapter 30 4

Electric flux

∫ ⋅= AdBΦrr

B ∫ ⋅= AdEΦrr

Magnetic flux

Surface defined by a conductive loop Closed surface

(Gaussian surface)

(N m2/C)(T m2)

Units: 1 T m2 = 1 weber = 1 Wb

θBAΦ cosB =if B is uniform and surface is flat.

Magnetic Flux

PHY2049: Chapter 30 5

Faraday’s Law (Law #3 of E&M)

dtΦdN Bε −=

emf

To avoid errorsUse Faraday’s law to calculate only the magnitude of emfUse Lenz’s law to find the direction

# of turns of the loop

Flux through the loop

PHY2049: Chapter 30 6

Same as the negative sign in Faraday’s lawLenz’s law: Direction of induced emf is such that resulting current opposes change in ФB.

Let’s examine three ways to change ФB through a coil

Change BChange area of the coil (motional emf)Change angle θ of the coil with respect to B (motional emf) – principle of the generator

Lenz’s Law

PHY2049: Chapter 30 7

Q1 Is the induced emf and current clockwise or counterclockwise?

Q2 What does the ammeter read, when the magnet is held in place?

Clockwise

ZeroQ3 What happens while the magnet is being pulled back? Counterclockwise emf and currentQ4 What happens if the S pole of the magnet is pushed toward the loop?

Counterclockwise emf and current

Changing B

N

S

PHY2049: Chapter 30 8

B field points into screen. Is induced emfclockwise or couterclockwise?

Changing Area

v

PHY2049: Chapter 30 9

Another Example

What is the direction of induced emf?(a) Clockwise(b) Counterclockwise(c) No emf

I

pullRHR #2

RHR #3 and Lenz

PHY2049: Chapter 30 10

Current i due to emf receives force from B

Force required to pull the loop

Power (work per time) required to pull the loop

Power dissipated in the wire as heat

iLBF =

iLBF =req

Motional emf and Energy

Agrees!

LvBε =||

Ri ε ||=

( )( )

( )RLvBvF

FP

2

reqreq

req timedistance

===

( )RLvBR

RLvBRiP

222

diss =

==

F

i

i

PHY2049: Chapter 30 11

Electric Power Generation… when Faraday was endeavouring to explain to Gladstone (Chancellor of the Exchequer) and several others an important new discovery in science, Gladstone's only commentary was “but, after all, what use is it?” “Why, sir,” replied Faraday, “there is every probability that you will soon be able to tax it!”

W. E. H. Lecky, Democracy and Liberty (Longmans Green, London, 1899)