March 7 Physics 54 Lecture Professor Henry Greenside

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March 7 Physics 54 LectureProfessor Henry
Greenside
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Outline

• Chapter 28
• Amperes law deducing B for complicated currents
  that have a symmetry.
• Application of Amperes law to wires, solenoids
  and toroids.
• Reminder we are skipping Sections 28-6, -7, -9,
  and -10. But please read Section 28-8 which has
  some useful and interesting qualitative
  information about solenoids.

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Key Formulas from the Previous Lecture
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PRS Loop Pushed Toward Wire I
I

• A closed rectangular loop of wire is pushed with
• constant speed toward a wire carrying a current I
  
• as shown. Then
• Nothing happens to the loop.
• A current flows clockwise in the loop.
• A current flows counterclockwise in the loop.
• I dont know what to do here

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PRS Current Loop Near Wire
I1
I2

• A closed rectangular loop of wire carrying a
  clockwise
• current I2 is near a vertical wire with current
  I1. Then
• The loop will move to the right.
• The loop will move to the left.
• The loop will move up.
• The loop will move down.
• The loop will rotate without its center moving.

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At the Whiteboard

• Detailed explanation of what happens when you
  push a loop toward a wire carrying a current a
  current starts to flow in the loop and a net
  force appears that opposes the direction of the
  pushing.
• A straight wire segment being pushed through a
  magnetic field acts like a battery with voltage
  difference vLB, where v is the speed of the wire,
  L is the length of the wire, and B is the
  magnitude of uniform magnetic field.
• Discussion of Amperes law the magnetic analog
  of Gausss law for deducing the magnetic field of
  complicated but symmetric currents.
• Discussion of line integral on left side of
  Amperes law.
• Applications of Amperes law to a single wire, to
  a hollow wire, and to a solenoid.

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Clarification for Amperes LawWhat is meant by
positive and negative currents?
Amperes law says that the line integral of the
magnetic field along some imaginary
(mathematical) closed loop is equal to some
constant times the total current enclosed. But
how do we choose a positive or negative sign for
the currents that pass through the loop? The
answer is to use the right hand rule on the loop
if in your mind you grasp the loop with your
right hand so that your thumb points in the
direction that your are tracing out the loop,
then your fingers curl into the inside of the
loop in the direction of positive currents. If
you think about it, this makes sense since it
gives the right answer when applied to a circular
loop centered on a straight wire carrying a
current I.
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Solenoids A Practical Way to Produce A Uniform
Magnetic Field
Will use Amperes law at whiteboard to derive
this important relation. The quantity n is the
ratio of the number of windings N per length L of
the solenoid, I is the current that flows through
each coil of the solenoid. Use the right hand
rule for a single coil to deduce the direction of
the magnetic field lines inside the solenoid.
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Helmholtz Coils A Quick and Easy Solenoid
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PRS Question Evaluation of a Line Integral
A
D
E
H
F
G
x
L
B
C
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Practice With Amperes Law B Field of A Current
Sheet

• Hammer a wire into a thin planar sheet of large
  width L and thickness d,
• and pass a current I through the wire uniformly
  so that you have a constant
• area current density jI/AI/(Ld).
• What direction is the magnetic field everywhere
  in space?
• How strong is the magnetic field everywhere in
  space?
• Note Everywhere means inside the sheet as well
  as outside the sheet