March 21 Physics 54 LectureProfessor Henry Greenside

Key Points from Previous Lecture

dt

dNEL loop

loops

:Law sFaraday'

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)cos(BA

LBEL vE

Today’s Topics

Finish Chapter 29:• Generators, motors, transformers, power lines.• Lenz’s law: how to predict the direction of an

induced current.

Faraday’s Law Explains How AC Generators Work

)sin())cos((

tNABdt

tABdN

dt

dN

E

Worked Example of Generator

A coil with area 2 m2 rotates in a 0.01 T magnetic field at a frequency f = 60 Hz. How many turns are needed to generate a peak voltage of 160 V?

turns21T) 010.0)(m Hz)(2.0 (602

V 160

2 2max

fAB

VN

πf ωtNAB 2 and )sin( E

PRS Question

For what orientation of this loop is the strongest mechanical force (torque) needed to turn the loop? (1) horizontal (2) vertical (3) 45o as shown (4) some other angle

Generation of Energy: Motion to Electricity

Motor is Generator Running BackwardsUnderstand From qv x B or IL x B Forces

Biological Motors Most Efficient Known

Kinesin and dynesin

Transformer: Valuable Application ofFaraday’s Law

Key insight: iron core makes flux p through primary coils on left equal to flux s through secondary coils on right. Therefore:

NV

or VV

so

, ,

ppsp

p

sssp

sps

sss

ppp

NVNN

dt

d

dt

d

dt

dNV

dt

dNV

Worked Transformer Example

A transformer for home use of a portable radio reduces 120 V ac to 9.0 V ac. The secondary coil contains 30 turns and the radio draws 400 mA. Calculate: a. the number of turns in the primary. b. the current in the primary. c. the power consumed.

W3.6A) V)(0.4 9(

A 0.03A) 4.0(400

30

turns40030V 9

V 120

ss

sp

sp

ss

pp

VIP

IN

NI

NV

VN

PRS Question

Why Transformers Are Useful

Worked Example: Power LinesAn average of 120 kW of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 . Calculate the power loss if the power is transmitted at (a) 240 V and (b) 24,000 V.

A.707500414.12I larger, iscurrent peak the

So kW. 120 power was average- time that the told werewe

since valuesrms are V and I assuch here quantities All :Note

W!10 A, 5 is (b)for Answer

kW 100) 4.0)(A) 500( losspower so

A 500V 240

kW 120

. Use

rmsmax

22

2

I

PI

RIP

V

PI

RIIVP

L

L

Edison Versus Westinghouse:DC Versus AC Power Transmission

Thomas Edison (1847-1931) (1846-1914)

Lenz’s Law (1833): How to Deduce The Minus Sign in Faraday’s Law

Changing magnetic flux in a coil causes an induced current toflow such that the new magnetic field created by the induced current opposes the change in flux.

How to use Lenz’s law to get direction of induced current:

1. Determine whether number of flux lines of some orientation through given area is increasing or decreasing.

2. Use right hand rule to choose direction of current in circuit that decreases or increases the number of flux lines in given direction, opposing trend of step 1.

Note: Lenz’s law is the conservation of energy in disguise. If current went wrong way, could create energy for free.

dt

dN loop

loops

E

Examples of Lenz’s Law

Will work these out on the white board: 1. Which way does induced current flow?2. What is direction of force acting on loop?

PRS Question

If magnetic field strength |B| increases at constant rate with same direction, 1. bar will move to right. 2. bar will move to left. 3. bar will not move at all.

Nothing Gold Can Stay By Robert Frost

Nature's first green is gold, Her hardest hue to hold. Her early leaf's a flower; But only so an hour. Then leaf subsides to leaf. So Eden sank to grief, So dawn goes down to day. Nothing gold can stay.