Physics 212 Lecture 15, Slide 1

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Physics 212 Lecture 15
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Music

• Who is the Artist?
• Diana Krall
• Norah Jones
• kd lang
• Madeline Peyroux
• Edith Piaf

CD
Great version of River (joni mitchell) with kd
lang
Haunting voice.. Highly Recommended.. Tough to
categorize (at New Orleans Jazzfest, they put her
in the traditional jazz tent (with Pete Fountain,
etc))
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Things you identified as difficult
Line integrals Amperes Law What does it
really mean??
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Amperes Law
I intoscreen
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Amperes Law
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Amperes Law
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Amperes Law
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Which of the following current distributions
would give rise to the B.dL distribution at the
right.
CD
A
C
B
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12
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Match the other two
CD
A
B
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Well the integral should be the same because the
equation does not depend on where the current is
enclosed in the circle but the strength of the
current enclosed. And since its the same current
enclosed then that means that the integral will
be the same.
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Ampere's law is concerned with only current that
is enclosed. In case 2 the currents are not
enclosed, so the integral is zero.
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using the right hand rule and curling your
fingers in the direction of current, your thumb
points in the direction of the B field with
happens to be to the right.
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Last Time
Two parallel horizontal wires are located in the
vertical (x,y) plane as shown. Each wire carries
a current of I 1A flowing in the directions
shown. What is the B field at point P?
y
y
I11A
B1
4cm
3cm
x
z
P
4cm
B2
I21A
Front view
Side view
P
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Follow-Up 1
y
Two parallel horizontal wires are located in the
vertical (x,y) plane as shown. Each wire carries
a current of I 1A flowing in the directions
shown. Suppose we double the distance along the
z-axis How does B change?
4cm
z
3cm
3cm
P
Q
OOOPS.. I goofed !!! I wanted to make the point
that you must be careful to use the right r BUT,
its a little more complicated than that
y
magnitude of B from each wire at Q (B1Q) is
greater than ½ of the magnitude of B from each
wire at P (B1P)
rQ ? 2rP
B1P
4cm
rQ lt 2rP
z
3cm
3cm
P
Q
B1Q
BUT THERES MORE !!
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Follow-Up 1
y
Two parallel horizontal wires are located in the
vertical (x,y) plane as shown. Each wire carries
a current of I 1A flowing in the directions
shown. Suppose we double the distance along the
z-axis How does B change?
4cm
z
3cm
3cm
P
Q
y
TO GET TOTAL B, WE NEED TO WORRY ABOUT THE ANGLES
B1P
qP
4cm
z
3cm
3cm
Q
P
qQ
B1Q
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One more thing on angles
It was nice to use a 3-4-5 triangle to simplify
the numbers, but unfortunately the angles in this
triangle are pretty close to 45o which can leave
a misleading perception (looks like B1 and B2
might be perpendicular).
The defining piece here is that each r is
perpendicular to its B The angle between the Bs
gets larger and larger as distance increases
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Calculation
I24A
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?
3cm
I11A
4cm
P
4cm

• Conceptual Analysis
• Complete cylindrical symmetry ? can use Amperes
  law to calculate B everywhere

• Strategic Analysis
• Calculate B for all values of r inside shell
• Set B 0 and solve for r

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Calculation
I24A
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?
3cm
I11A
4cm
P
4cm
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Calculation
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?
B determined by Ienclosed
Symmetry ? either along x or y
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Calculation
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?

• We know at (x,y) (0, 3mm)
• Inner conductor produces B in negative x
  direction
• Outer shell produces B in positive x direction
• At some value of r, these fields will cancel

You betcha !! Thats what Amperes Law is all
about !!
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Calculation
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?

• We know B 0 when the enclosed current is zero
• To find this radius, we will need to determine
  the current density in the shell.

The current is the amount of charge that passes
through a plane per unit time.
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Calculation
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?
What is the current density J in the shell?
J Current / Area
Area pR32 pR22
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Calculation
An infinite coax cable consists of solid cylinder
of radius R1 1mm and a shell with radii R2
2mm and R3 4mm. A current I1 1A (out of
screen) is uniformly distributed throughout the
inner cylinder while a uniform current I2 4A
(into screen) is uniformly distributed
throughout the shell. Where is B 0 in the
shell?
We want Ienclosed 0
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Follow-Up 1
Assume I1 5A while I2 remains equal to 4A.
At what value r0 does B 0 now?
If I1 gt I2, then it is impossible for the
current in the shell (I2) to cancel I1
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Follow-Up 2
Assume I1 1A and I2 4A again. What does Bx
at r (0,y) look like between r 0 and r R2?
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Follow-Up 2
y
x
x
x
x
x
x
R2
.
.
.
x
.
x
Assume I1 1A and I2 4A again. What does Bx
at r (0,y) look like between r 0 and r R2?
x
x
x
x
x
x
R3
x
(A)
(B)
(C)
(D)
(E)
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CD
Most confident
Least confident