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Today’s Concept: What Causes Magnetic Fields Physics 2112 Unit 14 Unit 14, Slide 1.

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Presentation on theme: "Today’s Concept: What Causes Magnetic Fields Physics 2112 Unit 14 Unit 14, Slide 1."— Presentation transcript:

1 Today’s Concept: What Causes Magnetic Fields Physics 2112 Unit 14 Unit 14, Slide 1

2 Compare to Electric Fields Unit 14, Slide 2 In the same direction as r 12 Perpendicular to r 12 v out of the screen

3 Unit 14, Slide 3 Biot-Savart Law B field from one moving charge But remember from previous slides B field from tiny of current carrying wire.

4 What is the magnetic field a distance y o away from a infinitely long wire of current I? Direction: Thumb: on I Fingers: curl in direction of B Example 14.1 (Infinite wire of current) Unit 14, Slide 4  Conceptual Plan  Strategic Analysis Done in prelecture in detail Integrate (Similar to E field for infinite line of charge) Use Biot-Savart Law

5 Unit 14, Slide 5 Main Idea  

6 Current I OUT r Magnitude: B Example 14.1 (answer) Unit 14, Slide 6 Remember:

7 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?   120 o

8 Example 14.3 (From Loop) Unit 14, Slide 8 yoyo 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 y o above the plane of the loop in the center? a P x x  Bcos  

9 Force Between Current-Carrying Wires Unit 14, Slide 9 I1I1 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 X X X X X X X X X I2I2 F

10 I towards us Another I towards us F Conclusion: Currents in same direction attract! I towards us  Another I away from us F Conclusion: Currents in opposite direction repel! d B B d Force Between Current-Carrying Wires Unit 14, Slide 10

11 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 I 1 = 5A I 2 = 10A 10cm 50cm

12 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 X B F Unit 14, Slide 12

13 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

14 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

15 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!

16 Checkpoint 2: Force on a loop A.the forces are in opposite directions B.the net forces are the same. C.the net force on the loop is greater than the net force on the wire segment D.the net force on the loop is smaller than the net force on the wire segment E.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?

17 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)

18 B on axis from Current Loop I Resulting B Field Current in Wire Electricity & Magnetism Lecture 14, Slide 18

19 What about Off-Axis ? Biot-Savart Works, but need to do numerically See Simulation! Unit 14, Slide 19

20 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 SN S 2) Look like bar magnets

21 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 Unit 14, Slide 21

22  Conceptual Analysis Each wire creates a magnetic field at P B from infinite wire: B   0 I / 2  r Total magnetic field at P obtained from superposition y x. z I 1  1A Front view Side view  Strategic Analysis Calculate B at P from each wire separately Total B = vector sum of individual B fields I 2  1A 4cm y P 3cm Example 14.2 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 ? Unit 14, Slide 22

23 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. Use Biot-Savart Law

24 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!


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