physics 2112 unit 14
DESCRIPTION
Physics 2112 Unit 14. Today’s Concept: What Causes Magnetic Fields. Compare to Electric Fields. v o ut of the screen. In the same direction as r 12. Perpendicular to r 12. Biot-Savart Law. B field from one moving charge. But remember from previous slides. - PowerPoint PPT PresentationTRANSCRIPT
Today’s Concept:What Causes Magnetic Fields
Physics 2112Unit 14
20 ˆ
4 rrsdIBd
Unit 14, Slide 1
Compare to Electric Fields
Unit 14, Slide 2
212
120 ˆ4 r
rvqB
212
12ˆ41
rrqE
o
In the same direction as r12 Perpendicular to r12
v out of the screen
ATm /104 70
Unit 14, Slide 3
20 ˆ
4 rrsdIBd
212
120 ˆ4 r
rvqB
Biot-Savart Law
B field from one moving charge
avgqnAvI But remember from previous slides
B field from tiny of current
carrying wire.sd
What is the magnetic field a distance yo away from a infinitely long wire of current I?
Example 14.1 (Infinite wire of current)
20 ˆ
4 rrsdIBd
Unit 14, Slide 4
Conceptual Plan
Strategic AnalysisDone in prelecture in detail
Integrate
(Similar to E field for infinite line of charge)
Use Biot-Savart Law
Unit 14, Slide 5
Main Idea
20 ˆ
4 rrsdIB
)()sin(*
4 220
oyxdxI
f
Q
r̂sdf
sd
Current I OUTrMagnitude:
B
Example 14.1 (answer)
rIB
2
0 •
Unit 14, Slide 6
ATm /104 70
Remember:
rE
o 2
Example 14.2 (B field from hexagon)
Unit 14, Slide 7
b
A current, I, flows clockwise through a hexagonal loop of wire. The perpendicular distance between each side and the center of the loop is b.
What is the magnetic field in the center of the loop?
f
Q r̂sd
f
sd
120o
Example 14.3 (From Loop)
Unit 14, Slide 8
yo
A current, I, flows clockwise through a circular loop of wire. The loop has a radius a.
What is the magnetic field at a point P a distance yo above the plane of the loop in the center?a
P
x
x
Q
BcosQ
Q
Force Between Current-Carrying Wires
BLIF
212
1212 2I
dLIF o
Unit 14, Slide 9
I1 rIB
2
10X X X X X X X X X X X X X X X X X X XX X X X X X X X X X X X X
X X X X X X X X X X X X
X X X X X X X X X X
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
I2
F
I towards us • • Another I towards usF
Conclusion: Currents in same direction attract!
•
I towards us
Another I away from usF
Conclusion: Currents in opposite direction repel!
d B
Bd
Force Between Current-Carrying Wires
BLIF
212 1212 2I
dLIF o
Unit 14, Slide 10
Example 14.4 (Two Current Carrying Wires)
Two current carrying wires a 10cm apart for a length for 50cm. Wire 1 carries 5A and Wire 2 carries 10A with both current to the left.
What is the magnitude and direction of the force on wire 2 due to wire 1?
Unit 14, Slide 11
I1 = 5A
I2 = 10A10cm
50cm
CheckPoint 1A
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
XB
F
Unit 14, Slide 12
CheckPoint 1B
What is the direction of the torque on wire 2 due to wire 1?
Uniform force at every segment of wire
No torque about any axis
Unit 14, Slide 13
A) Up B) Down C) Into Screen D) Out of screen E) Zero
CheckPoint 3A
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
Unit 14, Slide 14
CheckPoint 3B
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
Unit 14, Slide 15
LET’S DRAW A PICTURE!
Checkpoint 2: Force on a loop
A. the forces are in opposite directionsB. the net forces are the same.C. the net force on the loop is greater than the net force on the wire segmentD. the net force on the loop is smaller than the net force on the wire segmentE. there is no net force on the loop
A current carrying loop of width a and length b is placed near a current carrying wire.
How does the net force on the loop compare to the net force on a single wire segment of length a carrying the same amount of current placed at the same distance from the wire?
Checkpoint question
Current flows in a loop as shown in the diagram at the right. The direction is such that someone standing at point a and looking toward point b would see the current flow clockwise.
What is the orientation of the magnetic field produced by the loop at points a and b on the axis?
(A)
(B)
(C)
(D)
B on axis from Current Loop
..I
Resulting B Field
Current in Wire
Electricity & Magnetism Lecture 14, Slide 18
What about Off-Axis ?Biot-Savart Works, but need to do
numerically
See Simulation!
Unit 14, Slide 19
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 C) There is no force between them
Two Current Loops
Unit 14, Slide 20
Two ways to see this:
1) Like currents attract
N S N S
2) Look like bar magnets
1. ANY CROSS PRODUCT
2. Direction of Magnetic Moment
Thumb: Magnetic Moment
Fingers: Current in Loop
3. Direction of Magnetic Field from Wire
Thumb: Current
Fingers: Magnetic Field
Right Hand Rule Review
BvqF
BLIF
Fr
B
20 ˆ
4 rrsdIBd
Unit 14, Slide 21
Conceptual AnalysisEach wire creates a magnetic field at P
B from infinite wire: B 0I / 2rTotal magnetic field at P obtained from superposition
y
x
.
z
I1 1A
Front view Side view
Strategic AnalysisCalculate B at P from each wire separatelyTotal B = vector sum of individual B fields
I2 1A
4cm
4cm
y
P3cm
Example 14.2Two 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?
Unit 14, Slide 22
If I = 6A, what is the magnitude of the magnetic field at point P?
Example 14.5 (Curved Loop of Wire)
P
20cm
12cm Conceptual Plan
Strategic Analysis
Integrate both loops
Note straight sections cancel out.
20 ˆ
4 rrsdIBd
Use Biot-Savart Law
Good News!!!!!
Unit 14, Slide 24
Remember how we used Gauss’ Law to avoid doing integral in E
field?
We got similar law for B fields!