Electromagntic Induction

8/8/2019 Electromagntic Induction

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The magnetic forces

Like poles repel each other, andunlike poles attract.


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The magnetic field

A magnetic field exists in the region around a magnet.

Them

agnetic field is a vector that has bothmagnitude and direction.

The direction of the magnetic field at any point inspace is the direction indicated by the north poleof a small compass needle placed at that point.


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The magnetic field line

The lines originate from the north pole and end on thesouth pole; they do not start or stop in midspace.

The magnetic field at any point is tangent to the

magnetic field line at that point. The strength of the field is proportional to the number

of lines per unit area that passes through a surfaceoriented perpendicular to the lines.

The magnetic field lines will never come to cross each

other.


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What Produces a Magnetic Field?

Moving electrically charged particles, such as a current,produce a magnetic field

Permanent magnet. Elementary particles such as electrons

have an intrinsicm

agnetic field around them

. Them

agneticfields of the electrons in certain materials add together togive a net magnetic field around the material. Such additionis the reason why a permanent magnet has a permanentmagnetic field. In other materials, the magnetic fields ofthe electrons cancel out, giving no net magnetic field

surrounding the material


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Magnetic force on a Charged Particle

When a charge is placed in a magnetic field, itexperiences a magnetic force if two conditions aremet:

1. The charge must be moving. No magnetic force acts ona stationary charge.

2. The velocity of the moving charge must have acomponent that is perpendicular to the direction of thefield.


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Magnetic force on a Charged Particle

Right-Hand Rule

The force acting on a chargedparticle moving with velocity through

a magnetic field is alwaysperpendicular to and .


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The Definition of Magnetic Field

where F is the magnitude of the magnetic force on apositive test charge q0 , v is the velocity of the chargewhich makes an angle U with the direction of themagnetic field.

The magnetic field B is a vector, and its direction isdirection is along the zero-force axis.

The magnitude B of the magnetic field at any pointin space is defined as

SI Unit of Magnetic Field:


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Differences of ELECTRIC AND

MAGNETIC FIELDS

1. Direction of forces The electric force on a charged particle (both

moving and stationary) is always parallel (oranti-parallel) to the electric field direction.

The magnetic force on a moving charged particleis always perpendicular to both magnetic fieldand velocity of the particle. No magnetic forceon a stationary charged particle.


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2. THE WORK DONE ON ACHARGED PARTICLE:

The electric force can do work onthe particle.

The magnetic force cannot do work

and change the kinetic energy of thecharged particle.


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The motion of a charged particle in a

constant magnetic field A charged particle in a

constant magnetic field willdo uniform circular motion

The radius of the circle is


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Magnetic Force on a Current-Carrying Wire


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If the magnetic field is notperpendicular to the wire, as inFig, the magnetic force is given

by

Define as a length vectorthathas magnitude L and is directed along the

wire segment in the direction ofthe (conventional) current.

Magnetic Force on a Current-Carrying Wire


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Magnetic Dipole in a Magnetic Field

The torque on the coil due to a magnetic field

The magnetic potential energy

If an appliedtorque to rotates a

magnetic dipole from an initial

orientation to another

orientation , then work Wa

is done

on the dipole by the appliedtorque is


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A DC electric motor


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Walker, Chapter 23Magnetic Flux and

Faradays Law ofInduction


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Magnetic Induction

Demonstrations Ammeter for overhead projector which

measures the current in a coil. Under what

circumstances is a current induced in the

coil? How do we get the largest current?

Disk launcher with

Al ring

Slit ring

Fe ring

Bakelite ring

coils with bulbs


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Chapter 22: Electric currents (in a wire,in a plasma, in a fluid solution, inside anatom) produce a disturbance in thesurrounding space called the magneticfield. This magnetic field produces

forces on any other macroscopic ormicroscopic currents.

Example: MRI: Magnetic field (severalTesla) from superconducting solenoidinduces a net alignment of themicroscopic currents inside each andevery proton at the center of theHydrogen atoms in your body

Electric Currents produce Magnetic Fields


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Induced emf (Voltage)

from changing Magnetic

FluxElectric currents produce magnetic fields.

19th century puzzle: Can magnetic fieldsproduce currents?

A static magnet will produce no current in astationary coil.

Faraday: If the magnetic field changes, or ifthe magnet and coil are in relative motion,

there will be an induced emf (and thereforecurrent) in the coil.

Key Concept: The magnetic flux through thecoil must change. This will induce an emfI inthe coil, which produces a current I = I/R in the

coil.


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Magnetic Flux

For a loop of wire (not necessarily circular)with area A,in an external magnetic fieldB, the

magnetic flux is: * ! !B B A BAcosU

SIunits of Magnetic Flux:1 Tm2 = 1 weber = 1

Wb

A = area of loop

U = angle between B and

the normal to the loop


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Current

Loop

y

y

yy

y yy

y

Reminder: Current in a loopgenerates a magnetic field (and

therefore magnetic flux). The

magnetic field generated by this

current is into the page inside the

loop, and out ofthe page outside theloop.

RHR: Point your (right-hand) thumb along the direction ofthe current.

Your fingers point in the direction ofthe magnetic field (andthe

magnetic flux).

OR

Curl your fingers aroundthe loop in the direction ofthe current. Your

(right-hand) thumb points in the direction ofthe magnetic fieldthis

current generates throughthe loop.


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Faradays Law of

InductionFaradays Law: The instantaneous emf in acircuit (w/ Nloops) equals the rate of changeof magnetic flux through the circuit:

if

if

ttNtN

**

!(

(*

!I

The minus sign indicates the direction ofthe induced

emf. To calculate the magnitude:

if

if

ttN

tN

**!

(

(*!I


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Examples of Induced

CurrentAny change of current in primary induces a current in secondary.


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Induced

Current The current in the primary polarizes the

material of the core.

The magnetic field of the primary solenoid isenhanced by the magnetic field produced bythese atomic currents.

This magnetic field remains confined in the ironcore, and only fans out and loops back at theend of the core.

Any change in the current in the primary(opening or closing switch) produces achange in the magnetic flux through thesecondary coil. This induces a current inthe secondary.


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Induction by

Relative Motion When a permanent magnet

moves relative to a coil, themagnetic flux through thecoil changes, inducing an

emf in the coil. In a) the magnitude of the

flux is increasing

In c) the flux is decreasingin magnitude.

In a) and c) the induced

current has opposite sign.

v

v


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Lenzs Law

Lenzs Law: An induced current always flows in adirection that opposes the change that caused it.

In this example the magnetic field in

the downwarddirection throughthe

loop is increasing. So a current is

generated in the loop whichproduces an upward magnetic field

inside the loop to oppose the

change.

Magnet moving down

towar

dloop

N

S

Induced current

InducedB field


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Generators

A generatorconverts mechanicalenergy to electrical energy. Consider acurrent loop which rotates in aconstant magnetic field:

The magnetic flux through the loopchanges, so an emf is induced.

If a loop of area A with Nturns rotateswith angular speed [(period of

rotation = T[) in a constant Bfieldthen the instantaneous induced emf is:

I!NBA[sin([t)

If this loop is part of a circuit, this emf

will induce an Alternating Current (AC)


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GeneratorA coil of wire

turns in amagnetic field.

The flux in the coil

is constantly

changing,

generating an emfin the coil.


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28-1 Magnetic Field Due

to a Straight Wire

B =

The value of the constant Q0, which

is called the permeability of free

Q0

2T

I

r

Experimentallydetermined equation.

Perpendicular

distance from wire to

point at which B is to

be determined.

Current in wire


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Direction ofB


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Example 28-4

Field inside and outside a wire.A long straight cylindrical wire

conductor of radius R carries a

current I of uniform current

density in the conductor.

Determine the magnetic field at

(a) points outside the conductor (r

> R), and (b) points inside theconductor (r < R). Assume that r,

the radial distance from the axis,

is much less than the length of


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Solenoid


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B is essentially zerooutside the solenoid.

Solenoid


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NoB along line integral


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Line integral perpendicular toB


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Line integral parallel to B


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Line integral perpendicular toB


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Solenoid


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FaradaysLaw

In our previous result, we said that the inducedEMF was equal to the time rate ofchange of

magnetic flux through a conducting loo p. This,

rewrittens

lightly, is

c

alled Faradays Law:

Why the minussign?

tEMF

(

(*!


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FaradaysLaw

Michael Faraday

1791 1867

English physicist

and mathematician


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FaradaysLaw: the Generator

A coil rotates with a constant angularspeed in amagnetic field.

but Jchanges

with time:

t

EMF

(

(*!

JcosAB!*

t[J!


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Mutual Inductance: Transformers

A transformeris twocoils wound around a

common iron core.


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Mutual Inductance: Transformers

The self-induced voltage in the primary is:

Through mutual induction, and EMF appears in

the secondary:

Their ratio:

tEMF PP

(

(*!

tNSS

(

(*!

P

S

P

S

P

S

N

N

tN

tN

!

(

(*

((*

!


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Inductors and Stored Energy

In general, a volume in which a magnetic field

exists has an energy density (energy per unit

volume) stored in the field:

0

2

2volume

energydensityenergy

Q

B!!


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Electromagntic Induction