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Transcript of 18.1-18.6 my name is joe my name is joe my name is joe my name is joe my name is joe my name is joe

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    1. Add up the contribution of all point charges at this point

    V A =1

    4p 0qir ii

    q1 r 1

    q2 r 2

    A

    2. Travel along a path from point very far away to the locationof interest and add up at each step: E d

    l

    V A = E dl

    A

    q1

    q2

    A E

    dl

    Potential at a Certain Location

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    A

    Example: E = 0 inside a charged metal sphere, but V is not!

    Common PitfallAssume that the potential V at a location is defined by theelectric field at this location. E

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    A negat ive test charge Q = -0.6C was moved from point A topoint B In a uniform electric field E=5N/C . The test charge is at res t before and after the move. The distance between A andB is 0.5m and the line connecting A and B is perpendicular tothe electric field. How much work was done by the net externalforce while moving the test charge from A to B?

    A

    B

    0.5mE = 5 N/C

    A. 1.5JB. 0JC. 1.5JD. 3.0JE. 3.0J

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    After moving the -0.6C test charge from A to B, it was thenmoved from B to C along the electric field line. The test chargeis at rest before and after the move. The distance between Band C also is 0.5m. How much work was done by the netexternal force while moving the test charge from A to C?

    A. 1.5JB. 0J

    C. 1.5JD. 3.0JE. -3.0J

    A

    CB

    0.5m E = 5 N/C

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    +1.5 J of work was done by the net external force while movingthe -0.6 C test charge from B to C. The test charge is at rest before and after the move. What is the voltage differencebetween B and C, and at which point is the voltage larger?

    A. 2.5 V, voltage higher at B.B. 2.5 V, voltage higher at C.C. 0.9 V, voltage higher at B.D. 1.5 V, voltage higher at B.E. 1.5 V, voltage higher at C.

    A

    E = 5 N/C

    B

    0.5m

    C0.5m

    D

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    A compass needle turns and points in a particular direction

    there is something which interacts with it

    Magnetic field ( B): whatever it is that is detected by a compass

    Compass: similar to electric dipole

    Magnetic Field

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    Magnetic fields are produced by moving charges

    Current in a wire: convenient source of magnetic field

    Static equilibrium: net motion of electrons is zero

    Can make electric circuit with continuous motion of electrons

    The electron current ( i) is the number of electrons per secondthat enter a section of a conductor.

    Counting electrons: complicated

    Indirect methods:measure magnetic fieldmeasure heating effect

    Electron Current

    Both are proportional to the electron current

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    Imagine an electric circuit:

    What is the effect on the compass needle?

    What if we switch polarity?

    What if we run wire under compass?

    What if we change the current or there is no current in the wire?

    The Magnetic Effects of Currents

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    Experimental results: The magnitude of B depends on the amount of current A wire with no current produces no B B is perpendicular to the direction of current B under the wire is opposite to B over the wire

    Oersted effect: discovered in 1820 by H. Ch. rsted

    How does the field around a wire look?

    The Magnetic Effects of Currents

    Hans Christian rsted(1777 - 1851)

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    Principle of superposition: wire Earthnet B B B +=

    What can you say about the magnitudes of B Earth and Bwire ?

    What if B Earth were much larger than Bwire ?

    The Magnetic Effects of Currents

    The moving electrons in a wire create a magnetic field

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    A current-carrying wire is oriented N-S and laid on top of acompass. The compass needle points 27 o west. What is themagnitude and direction of the magnetic field created by thewire Bwire if the magnetic field of Earth is B Earth = 2

    10 -5 T(tesla).

    wire Earthnet B B B +=

    qtan Earthwire B B =

    27tan1025

    =

    Twire BT5101 wire B

    Exercise

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    Nikola Tesla (1856-1943)High tension coil demonstration

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    A B = A x A y A z

    B x B y B z

    =

    A y B z A z B y A z B x A x B z A x B y A y B x

    =

    i

    j

    k

    A x A y A z B x B y B z

    = A y B z A z B y( )

    i A x B z A z B x( )

    j + A x B y A y B x( )

    k

    Calculate magnitude:

    A B = A Bsin q

    Right-hand rule

    The Cross Product

    Calculate direction:

    2

    0

    4 r

    r vq B

    =

    p

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    Question

    W h a t i s t he d ir e ct i o n o f

    < 0 , 0 , 3 > x < 0 , 4 , 0 > ?

    A ) +x B ) x C ) +y D ) y E ) z er o m ag n it u d e

    A

    B A =< 0,0,3 > ; B =< 0,4,0 >

    0 0 30 4 0

    = (0 12)

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    What is B straight ahead?

    2

    0

    4 r

    r vq B

    =

    p

    What if the charge is negative?

    Exercise

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    2

    0

    4 r r vq

    B

    =p

    v

    r B1

    B2

    B3

    Which is larger, B1 or B3 ?

    Which is larger, B1 or B2 ?

    Distance Dependence

    B =

    0

    4pqvr 2

    sin q

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    2

    0

    4 r r vq

    B

    = p

    v

    r B1

    v

    r B

    v

    r B1

    Magnetic field depends on qv: Positive and negative charges producethe same B if moving in oppositedirections at the same speed

    For the purpose of predicting B wecan describe current flow in terms of

    conventional current

    positive

    moving charges.

    Moving Charge Sign Dependence

    B =

    0

    4pqvr 2

    sin q+

    -

    -

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    QuestionAn electron passing through the origin is traveling at a constantvelocity in the negative y direction. What is the direction of themagnetic field at a point on the posi ti ve z axis?

    A) -x

    B) +xC) -zD) +zE) No magnetic field

    x

    z

    y

    v

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    What would the direction of conventional current have to be?

    A current-carrying wire lies ontop of a compass. What is thedirection of the electron currentin this wire?

    Exercise

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    Electric fields: produced by charges

    Magnetic fields: produced by moving charges

    charged tape

    Any magnetic field?0

    4 20 =

    =

    r r vq B p

    0

    4 20

    =

    r

    r vq

    B p

    Frame of Reference

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    20

    4 r r vq B

    = p

    Must use the velocities of the charges as you observe them in

    your reference frame !

    There is a deep connection between electric field and magnetic

    fields (Einstein

    s special theory of relativity)

    Frame of Reference

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    If we suddenly change the current in a wire:Magnetic field will not change instantaneously.

    Electron and positron collide:Produce both electric and magnetic field, these fields existeven after annihilation.

    Changes propagate at speed of light

    2

    0

    4 r r vq

    B

    =p

    There is no time in Biot-Savart law: Speed of moving charges must be small

    Retardation

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    A steady flow of charges in one direction will create amagnetic field. How can we cause charges to flow steadily?

    Need to find a way to produce and sustain E in a wire.

    Use battery

    Electron Current

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    nelectrons

    m 3

    A m

    2

    ( ) v m

    s

    t s( ) = nAv t electrons

    Electron current: i =# electrons

    s= nAv

    mobileelectron

    density

    wireCross sectional

    area

    Averagedrift

    speed

    Electron Current

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    Typical electron current in a circuit is ~ 10 18 electrons/s.What is the drift speed of an electron in a 1 mm thick copperwire of circular cross section?

    328104.8 mnvnA=s

    electrons#

    A =p D2

    4

    3.14 1 10 3 m( )2

    4= 8 10 7 m 2

    v =10 18 s -1

    nA

    10 18 s -1

    8.4 10 28 m 3( )8 10 7 m 2( ) = 1.5 10 5 m/s

    Typical Mobile Electron Drift Speed

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    m/s5105.1 =vHow much time would it take for a particular electron to movethrough a piece of wire 30 cm long?

    hours!sm/s

    m5.5102

    105.1

    30 45

    =

    ==

    .v s

    t

    How can a lamp light up as soon as you turn it on?

    Typical Mobile Electron Drift Speed

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    Observing magnetic field around copper wire: Can we tell whether the current consists of electrons or positive

    holes

    ?

    In some materials current moving charges are positive: Ionic solution

    Holes

    in some materials (same charge as electron but +)

    2

    0

    4 r

    r vq B

    =

    p

    2

    0

    4 r

    r ve B

    =

    p

    =

    0

    4p

    e( ) v( ) r

    r 2

    Conventional Current

    The prediction of the Biot-Savart law is exactly the same in either case.

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    2

    0

    4 r

    r ve B

    =

    p

    =

    0

    4p

    e( ) v( ) r

    r 2

    Metals: current consists of electronsSemiconductors:

    n-type electrons

    p-type positive holes Most effects are insensitive to the sign of mobile charges:introduce conventional current :

    vnAqiq I ==

    Conventional Current

    Units: C/s A (Ampere)

    Andr Marie Ampre(1775 - 1836)

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    A typical electron current in a circuit is 10 18 electrons/s.What is the conventional current?

    I = q i = 1.6 10 19 C( )10 18 s -1( ) = 0.16 A

    Exercise

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    Superposition principle is valid

    Bi = 04

    qivi

    r ir i

    2

    B = Bii

    = 04

    qivi

    r ir

    i

    2i

    =

    ir r vq

    B 1

    4 20

    l nAr

    r vq B

    =

    2

    0

    4

    vnAqiq I ==

    20

    4 r r l I

    B

    =

    The Biot-Savart law for ashort length of thin wire

    The Biot-Savart Law for Currents

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