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Today:

Chapter 25 (Magnetic Induction)

Electromagnetic Induction

•^

Voltage can be induced (created) by a changingmagnetic field.

•^

C.f.

last chapter: currents produce magnetic field, i.e.

electricity produces magnetic fields.The reverse is true too! Magnetic fields can produceelectricity.(Exploited today in effective electricity transmissionacross world)

Electromagnetic induction cont.

•^

Relative

motion is needed: Voltage

is induced either

-^

if magnet is moved near stationaryconductor,

or

• if conductor is moved near stationary

magnet

-^

The voltage induced creates a current that in turn, has a

magnetic field – this

repels

the original magnet that induced the

•^ voltage

The faster the motion, the greater the voltage. If move too

slowly, hardly any voltage.

Recall ch. 24

The key point is that the conductor lies in a region where the magnetic fieldchanges

Electromagnetic induction cont.

Eg.

DEMO:

Drop a magnet down a copper or aluminum pipe. It

takes longer to fall down than an unmagnetized object! Eg. This is why it is hard to push a magnetdown into a coil of many loops – large voltageinduced, so large current induced, so largemagnetic field associated with this, so largerepulsion with original magnet.

http://www.youtube.com/watch?v=sPLawCXvKmg

Clicker Question

Can current flow around a wire loop which is not connected

to any battery or power source?

A)

Yes, generally current will flow

B)

Yes, if the loop lies in a magnetic field

C)

Yes, if the loop lies in a changing magnetic field

D)

No, never, as this would violate energy conservation.

E)

No, never as this would violate charge conservation.

Answer: CFaraday’s law: Voltage, and therefore current, is inducedby a changing magnetic field

A Question

How could a light bulb near, but not touching, an

electromagnet be lit? Is ac or dc required?

recall, a current-carrying coil

If the bulb is connected to a wire loop that

intercepts changing magnetic field lines froman electromagnet, voltage will be induced thatcan illuminate the bulb. Need ac, since needchanging fields.

Eg. Idea behindtransformers, seeshortly:

Evenjust 1loopherewillwork.

Generators and Alternating Current

-^ Recall that induced voltage (or current)

direction

changes as to

whether magnetic field is increasing or decreasing (eg magnet beingpushed in or pulled out). In fact:frequency of the alternating voltage = frequency of changing magneticfield.

Generator:

when coil is rotated in a stationary

magnetic field: ac voltage induced by thechanging field within the loop.Note similarity to motor from Ch. 24: the onlydifference is that in a generator, the input isthe mechanical energy, the output is electrical.(other way around for motor).

Note, change in # field linesintersecting the loop area,as it rotates.

Generators cont.

Fundamentally, induction arises because of the force on movingcharges in a magnetic field (recall Ch.24):

Compare

motor effect

to

generator effect

Motor: currentalong wire,means movingcharges in magfield. Soexperienceforce perp tomotion and tofield, ie. upward.

Generator: wire(no initial current)moved downward,so electrons aremoving down infield, so feel forceperp to motion andto field ie alongwire, i.e. a current.(+ ions also feelforce, in opp dir.but not free tomove).

Transformers

Consider first the following arrangement of side-by-side coils:

The primary coil has a battery, sowhen switch is closed, current flowsin it, creating a sudden magneticfield that threads the secondary coil– inducing current pulse in it too. (Note no battery in secondary coil). Only brief though, since current insecondary only flows at the time theswitch in primary is opened or shut.

Question: Say the switch in primary coil is closed at time 0 and then openedagain after 5 seconds. What is (roughly) the behavior of the current in theprimary coil? the secondary coil?

Primary: current begins to flow at time 0, is constant for 5

seconds, and then drops to zero.

Secondary: current pulse at time 0 flows in one direction,

then goes to zero while the primary current is constant. Then pulse flows inopposite dir. when the switch is opened, and again goes to zero afterwards.

Transformers cont.

-^ To maintain current flow in the secondary coil, need always

changing

magnetic field

, i.e. always changing current in the primary coil –

use ac

• Moreover, can put an

iron core

through the coils, as this intensifies the

field (recall Ch.24) and so amplifies the current through the secondary,i.e. simple transformer looks like:

-^ Recall dependence on # coils (called #

turns

-- the field generated by the primary coil is greater if there are more

loops in it (Ch24, property of electromagnets)

-- the voltage induced in the secondary coil is greater if there are

more loops in it (Faraday’s law)

So…..

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Transformers and Power Transmission

•^

Because of energy conservation, if the voltage in the secondary isstepped up, the current must be correspondingly lower:

Power into primary = power out of secondary,

so

(voltage x current)

primary

= (voltage x current)

secondary

Recall: rate ofenergy transfer•

Transformers are behind the main reason why most electric power is acrather than dc: easy way of stepping up and down.• To transmit across large distances (i.e. cities…), want to minimize energyloss due to wire heating i.e. want

low currents

, so correspondingly

high

voltages

i.e. step up for transmission

• Power usually generated at 25 000 V, stepped up to 750 000V near thepower station for long-distance transmission, then stepped down in stagesto voltages needed in industry (eg 440 V) and homes (120 V).• EM induction thus is method for transferring energy between conductingwires. In fact, this is also behind radiant energy in the sun! (see later…)

Questions

If 120 V of ac are put across a 50-turn primary, what will be thevoltage and current output if the secondary has 200 turns, and isconnected to a lamp of resistance 80

(120 V)/50 = (?V)/(200), so? = 480 VCurrent = voltage/resistance = 480/80 = 6 A

What is the power in the secondary coil?

Power = voltage x current = 480 V x 6A = 2880 W

Can you determine the current drawn by the primary coil? If so, whatis it?

current = power/voltage, and power input = power out = 2880W

so, current = 2880/120 = 24 A

Self-induction

•^

Current-carrying loops in a coil interact with magnetic fields ofloops of other coils, but also with fields from loops of the same coil– called

self-induction

•^

Get a self-induced voltage, always in a direction

opposing

the

changing voltage that creates it. - called

back emf

(= back

electromotive force)

-^

We won’t cover this much, except to say that this is behind thesparks you see if you pull a plug out from socket quickly, whiledevice is on:

Consider here a long electromagnetpowered by a dc source. So have strongmag field through coils. If suddenly open aswitch (e.g. pulling the plug), the currentand the large field go to zero rapidly. Largechange in field

large induced voltage

(back emf) – this creates the spark (zap!).

Field Induction

•^

Fundamentally, a changing mag field produces an

electric field

, that

consequently yields voltages and currents.

-^

You don’t need wires, or any medium, to get fields induced.

-^

Generally, Faraday’s law is An electric field is created in any region of space in which amagnetic field is changing with time. The magnitude of the inducedelectric field is proportional to the rate at which the magnetic fieldchanges. The direction of the induced electric field is perpendicularto the changing magnetic field. Complementary to Faraday’s law (due to Maxwell):

just interchange

“electric” and “magnetic” in the law above!

i.e.

A magnetic field is created in any region of space in which anelectric field is changing with time. The magnitude of the inducedmagnetic field is proportional to the rate at which the electric fieldchanges. The direction of the induced magnetic field isperpendicular to the changing electric field.

-^

This beautiful symmetry is behind the physics of light andelectromagnetic waves generally!