Physics 212 Lecture 14, Slide 1

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Physics 212 Lecture 14
2
Music

• Who is the Artist?
• Tito Puente
• Buena Vista Social Club
• Louis Prima
• Freddie Omar con su banda
• Los Hombres Calientes

CD
In recognition of the end of an era (Fidel
Castro) Cuban Jazz !! Thanks to Ry Cooder for
bringing these guys to our attention !!
A YouTube clip from the 1999 Wim Wenders movie
of the same name.
3
Things you identified as difficult
Biot-Savart Law
Directions Cross Products
z
y
dB
r
dS
x
4
Biot-Savart Law
dB
I
5
Right Hand Rule for Cross Product
A
B
C
C A X B
6
Right Hand Rule for Cross Product
A
B
C
C A X B
7
Right Hand Rule for Cross Product
A
C
B
C A X B
8
A current carrying wire is oriented in the x-y
plane. Points A,B, C lie in the same plane as
the wire. Find the direction of B at the 3
points.
B
A
I
C
y
x
9
B
A
r
dS
I
C
y
x
10
B
A
r
dS
I
C
y
x
11
B
A
dS
r
I
C
y
x
12
A.
13
B.
14
C.
15

• You are free to bend a current carrying
  wire into any shape in the x-y plane. Can you
  find a shape such that the resulting magnetic
  field at the origin has a component in the x or
  the y direction?
• YES
• NO

CD
I
y
x
16
B) NO !! Since both ds and r are in the x-y
plane for any part of the wire, ds x r must be
perpendicular to the x-y plane !

I
y
x
r
dS
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More Handy Dandy Right Hand Rules
I
Current in Wire
Resulting B field
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More Handy Dandy Right Hand Rules
I
Resulting B field
Current in Wire
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More Handy Dandy Right Hand Rules
I
20
(No Transcript)
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End view
22
Two identical loops are hung next to each other.
Current flows in the same direction in both.
The loops will A) Attract each other
B) Repel each other
CD
1) Just like the parallel wire case we just
discussed (except bent).
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A) Attract each other
Current Loop
Two ways to see this
2) The B field from each is in the same direction
Resulting B field
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Last Time
A square loop of side a lies in the x-z plane
with current I as shown. The loop can rotate
about x-axis without friction. A uniform field B
points in the z direction. Assume a, I, and B
are known. How much work is required by an
external agent to move the coil from its intial
position to its final position as shown.
z
z
.
B
B
30
y
y
m
I
x
final
initial

• Work done by external agent -Work done by B
  field
• Change in potential energy -Work done by
  B field
• Therefore Work done by external agent Change
  in potential energy
• W DU U - 0 Ia2Bsin(30o)

q
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Follow-Up
From which of these possible initial states would
the work done by an external agent to move the
coil to the final state be zero ?
For W 0, we need Uinitial Ufinal
x
q
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Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view

• Conceptual Analysis
• Each wire creates a magnetic field at P
• B from infinite wire B m0I / 2pr
• Total magnetic field at P obtained from
  superposition

• Strategic Analysis
• Calculate B at P from each wire separately
• Total B vector sum of individual B fields

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Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view
28
Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view
3cm
90o
29
Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view

• What is the direction of B at P produced by the
  bottom current I2?

(A) (B)
(C) (D) (E)
90o
3cm
30
Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view

• What is the direction of B at P?

3cm
31
Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view

• What is r?
• r distance from wire axis to P

3cm
5cm
32
Calculation
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
4cm
3cm
x
z
P
4cm
I21A
Front view
Side view
y
4cm
z
3cm
P