Induced Voltages And Inductance

Chapter 20

Hans Christian Oersted

Introduction Oersted’s discovery was the first evidence of a link between electricity and magnetism.

Symmetry in Physics Symmetry in nature helps scientists to make new discoveries.

Generating Electricity Could magnetic fields produce electric currents? Joseph Henry made this discovery

Power plants were the result of his efforts

Induced emf And Magnetic Flux

Faraday’s experiment A current can be produced by a changing magnetic field.

20.1

Primary and Secondary Coils

A steady magnetic field in the primary coil cannot produce a current in the secondary coil.

Induced emf And Magnetic Flux

Magnetic flux The flux is proportional to the number of lines passing through the loop

Changes in the flux induce a change in the emf.

20.2

Magnetic Flux Formula

is the angle between the B field and

the normal to the plane of the loop

€

=BA = BAcosθ

Faraday’s Law of Induction

A simple demonstration Wire loop, galvanometer, magnet

20.4

Induced Current A current is set up in the loop as long as there is relative motion between the magnetic field and the loop. This is an induced current.

20.4

Faraday’s Law of Induction

The induced emf () in a circuit equals the rate of change of the magnetic flux through the circuit.

Formula for Faraday’s Law of magnetic induction

€

=−NΔΦB

Δt

Faraday’s Law of Induction

SinceA.cos

And = -N./t

Then = -N.A.cos/t

Lenz’s Law The induced current tries to maintain the original flux through the circuit. It sets up a magnetic field that opposes any change in the original magnetic field.

Applications of Faraday’s Law

Electric guitar Metal strings Pickup coil

Cruise control Ground fault interrupter (GFI)

Protects against electrical shock Where is it used? How does it work?

SIDS monitor

20.10a, 209, 20.8, 214, 20.5

Motional emf Motional emf is the emf induced in a conductor moving through a magnetic field. Example: A straight conductor moving through a magnetic field

20.8, 20.13

Formula:

€

V = El = Bl v

Motional emf A potential difference (V) is maintained across a conductor as long as there is motion through the field. If the direction of the motion is reversed, the polarity also reverses.

Motional emf Motion involving a closed conducting path Current flows through the circuit

162, 211

Important Formulas:

€

=t

= Bl v

€

I =ε

R=Bl v

R

Lenz’s Law Revisited Another example (Figure 20.17): A stationary conducting loop and a bar magnet

215, 20.13, 165

Applications of Magnetic Induction

Cassette tape recorders/players Magnetic tape Recording head Playback head

VHS recorders/players Computer hard drives

Questions

1 - 7

Pg. 689

AC Generators The alternating current (ac) generator

Converts mechanical energy to electrical energy

Has a coil rotating in a magnetic field Slip rings

Insure that the output voltage changes polarity Stationary brushes

20.20, 216

Types of Commercial Power Plants

Fossil Fuel Hydroelectric Nuclear

Total emf Formula for total emf:

Notet = andf (f = 60 Hz in USA)

is measured between the magnetic field and the normal to the loop.

Maximum emf occurs when the plane of the loop is parallel to the magnetic field

213

€

=NBAω sin(ωt)

DC Generators The direct current (dc) generator Uses a split ring or commutator

This insures that the output voltage does not change polarity.

20.22

Motors and Back emf A motor is the opposite of a generator. Because of Lenz’s Law, back emf is generated in a motor.

Back emf increases with rotational speed. Back emf tends to reduce current flow in the windings.

Maximum current is present when the motor starts up.

217

Back emf vs. Speed

Equation for back emf

€

=V − I ⋅R

Eddy Currents Eddy currents are circular currents which occur in a piece of metal when it moves through a magnetic field

Magnetic Damping The magnetic fields produced by the eddy currents try to prevent motion of the metal through the field.

Effects of Eddy Currents

The effects of eddy currents are undesirable in motors and generators. These effects can be reduced

Laminations are used

Laminations in an Armature

Self-Inductance A changing flux through the circuit arises from the circuit itself. This occurs in coils and solenoids

Solenoid Video

Self-Induced emf The self induced emf is proportional to the time rate of change of current

L is a constant representing the inductance of the device and is measured in Henries (H).

€

=−LΔI

Δt

Inductance Formula for inductance (L)

€

L =μoN

2A

l€

L =NΔΦ

ΔI

Inductors An inductor is a circuit element which is used to provide inductance.

Usually a closely wrapped coil of many turns

Inductance Inductance (L) is a measure of the opposition to the rate of change of current. Schematic symbol

20.27/20.28

RL Circuits RL time constant ()

The time that it takes for the current in the circuit to reach 63.2 % of its maximum value.

€

=L

R

Energy Stored In A Magnetic Field

Current flowing through a solenoid produces a magnetic field. The battery must do work to produce a current in a coil.

This energy is stored in the magnetic field of the coil.

37-1, 14, 78

€

PEL = 1

2LI2

Questions

8,10, 11, 13, 14

Pg. 689