Physics 212 Lecture 14, Slide 1

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Physics 212 Lecture 14
Biot-Savart Law
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How confident are you in your understanding of
the concepts presented in the prelecture? A  I
am confused by all of it. B  I understand a
little but I am confused by most of it. C  I
understand some parts and I am confused by other
parts. D  I understand most of itE  I
understand everything F I didn't view the whole
prelecture so I can't comment.
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Key Concepts

• Biot-Savart Law Gives direction and magnitude of
  the magnetic field due to an element of current

Todays Plan

• Review right hand rule for currents
• Forces Torques between wires
• Example problem

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B from infinite line of current
Magnitude
B
r
r distance from wire
Direction Thumb on I Fingers curl in
direction of B
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More Handy Dandy Right Hand Rules
I
Current in Wire
Resulting B field
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Currents Charges
A long straight wire is carrying current from
left to right. Two identical charges are moving
with equal speed. Compare the force on charge a
moving directly to the right, to the force on
charge b moving up and to the right at the
instant shown (i.e. same distance from the wire).
CD
v
v


(b)
(a)
I
r
r
F

• Fa gt Fb
• Fa Fb
• Fa lt Fb

Same q, v, B and q (90)
Forces are in different directions
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Adding Magnetic Fields
Two long wires carry opposite current
B
x
x
What is the direction of the magnetic field
above, and midway between the two wires carrying
current at the point marked X?
1) Left 2) Right 3) Up 4) Down 5) Zero
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Force between current-carrying wires
I towards us

Conclusion Currents in same direction attract!
Conclusion Currents in opposite direction repel!
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Preflight
What is the direction of the force on wire 2 due
to wire 1?
A) Up B) Down C) Into Screen D) Out of
screen E) Zero
Because the currents are going in the same
direction, there is an attractive force.
The cross product of the force(points down) with
the distance between the wires equals zero since
the two are parallel.
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Preflight
Lets see some tricky cases in lecture.
What is the direction of the force on wire 2 due
to wire 1?
A) Up B) Down C) Into Screen D) Out of
screen E) Zero
The asymmetrical fields left and right of wire 1
have equal and opposite net forces on wire 2.
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How do I know if the magnetic field is going in
and out if the field leaves the screen the same
amounts of time as the field enters the
screen???!!! AHH RIGHT HAND RULE FAILS!!! How is
torque involved in this????????? Oh my God this
stuff is hard!
Net Force is Zero!
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Preflight
What is the direction of the torque on wire 2 due
to wire 1?
A) Up B) Down C) Into Screen D) Out of
screen E) Zero
The right side is pushed in, while the left side
is pushed out. .
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B from current loop
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More Handy Dandy Right Hand Rules
I
Resulting B field
Current in Wire
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Two Current Loops
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
Two ways to see this

• Like currents attract.

2) Look like bar magnets
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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
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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

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

(A) (B)
(C) (D) (E)
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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

• What is the direction of B at P?

z
P
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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

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

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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
y
4cm
z
3cm
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Summary