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# Physics 2112 Unit 14

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

2. Compare to Electric Fields vout of the screen In the same direction as r12 Perpendicular to r12

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

4. Example 14.1 (Infinite wire of current) What is the magnetic field a distance yoaway from a infinitely long wire of current I? • Conceptual Plan Use Biot-SavartLaw • Strategic Analysis • Done in prelecture in detail • Integrate • (Similar to E field for infinite line of charge) Direction: Thumb: on I Fingers: curl in direction of B

5. Main Idea Q f

6. Example 14.1 (answer) Magnitude: B Current I OUT r • Remember:

7. Example 14.2 (B field from hexagon) 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? 120o b Q f

8. Example 14.3 (From Loop) 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? P yo a Q x BcosQ Q x

9. Force Between Current-Carrying Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1 X XXXXXXXXXXXXXXXXXX X XXXXXXXXXXXX X XXXXXXXXXXX X XXXXXXXXX F I2

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

11. Example 14.4 (Two Current Carrying Wires) 50cm I2 = 10A 10cm I1 = 5A 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?

12. CheckPoint 1A B X F 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

13. CheckPoint1B 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 Uniform force at every segment of wire No torque about any axis

14. CheckPoint 3A What is the direction of the force on wire 2 due to wire 1? Up B) Down C) Into Screen D) Out of screen E) Zero

15. CheckPoint 3B What is the direction of the torque on wire 2 due to wire 1? Up B) Down C) Into Screen D) Out of screen E) Zero LET’S DRAW A PICTURE!

16. Checkpoint 2: Force on a 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? the forces are in opposite directions the net forces are the same. the net force on the loop is greater than the net force on the wire segment the net force on the loop is smaller than the net force on the wire segment there is no net force on the loop

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

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

20. Two Current Loops S S N N 2) Look like bar magnets Two identical loops are hung next to each other. Current flows in the same direction in both. The loops will: Attract each other B) Repel each other C) There is no force between them Two ways to see this: 1) Like currents attract

21. Right Hand Rule Review 1. ANY CROSS PRODUCT 2. Direction of Magnetic Moment Fingers: Current in Loop Thumb: Magnetic Moment 3. Direction of Magnetic Field from Wire Fingers: Magnetic Field Thumb: Current

22. Example 14.2 . y 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. What is the B field at point P? I1= 1A 4cm 3cm x z P 4cm I2= 1A 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

23. If I = 6A, what is the magnitude of the magnetic field at point P? Example 14.5 (Curved Loop of Wire) 0 of 250 39 20cm 12cm P Conceptual Plan Use Biot-SavartLaw • Strategic Analysis • Integrate both loops • Note straight sections cancel out.

24. Good News!!!!! Remember how we used Gauss’ Law to avoid doing integral in E field? We got similar law for B fields!