1. Physics 212 Lecture 14, Slide 1 Physics 212 Lecture 14 Biot-Savart Law :05

2. Main Point 1 First, we introduced the Biot-Savart law, the fundamental law that allows us to calculate the magnetic field dB that is produced a distance r from a current segment Ids. The key features of the Biot-Savart law are that the magnitude of the field is proportional to the inverse square of the distance from the current segment, and the direction is given by a cross product. We applied this law to determine that the magnetic field produced by an infinite straight wire is proportional to the current it carries and falls of as 1 over R, the perpendicular distance from the wire. The direction of the field at any point on a circle of radius R from the wire is tangent to that circle with its sense determined by a right hand rule. Namely, if you place the thumb of your right hand in the direction of the current, your fingers will curl in the direction of the B field. Physics 212 Lecture 14, Slide 2

3. Main Point 2 Second, we calculated the force between two parallel current-carrying wires by determining the Lorentz force on the charge carriers in one wire due to the magnetic field produced by the other wire. We determined this force to be proportional to the product of the currents and inversely proportional to the separation between the wires. Physics 212 Lecture 14, Slide 3

4. Main Point 3 Finally, we investigated the magnetic field produced by a circular current carrying loop. We found that the field was directed along the axis of the loop, parallel to the loop’s magnetic dipole moment vector, and that the field was maximum at the plane of the loop and decreased with increasing z, the distance from the plane of the loop. Physics 212 Lecture 14, Slide 4

5. Physics 212 Lecture 14, Slide 5 Biot-Savart Law: :05 What is it? Fundamental law for determining the direction and magnitude of the magnetic field due to an element of current Fundamental law for determining the direction and magnitude of the magnetic field due to an element of current We can use this law to calculate the magnetic field produced by ANY current distribution BUT BUT Easy analytic calculations are possible only for a few distributions: Easy analytic calculations are possible only for a few distributions: Infinite Straight Wire Axis of Current Loop Plan for Today: Mainly use the results of these calculations!! GOOD NEWS: Remember Gauss’ Law? Allowed us to calculate E for symmetrical charge distributions NEXT TIME: Introduce Ampere’s Law Allows us to calculate B for symmetrical current distributions

6. Physics 212 Lecture 14, Slide 6 B from infinite line of current Current I OUT r = distance from wire r Magnitude: B :07 Integrating gives result Direction: Thumb: on I Fingers: curl in direction of B

7. 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 Physics 212 Lecture 14, Slide 7 Checkpoint 1 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 :18

8. Physics 212 Lecture 14, Slide 8

9. Checkpoint 2:24 A B C D E 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? 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 Physics 212 Lecture 14, Slide 9

10. Physics 212 Lecture 14, Slide 10

11. Physics 212 Lecture 14, Slide 11 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 :21

12. Physics 212 Lecture 14, Slide 12 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 :24

13. Physics 212 Lecture 14, Slide 13

14. Physics 212 Lecture 14, Slide 14 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). a)|F a |> |F b | b)|F a |= |F b | c)|F a |< |F b | v I v (a) r r (b) Currents + Charges

15. Physics 212 Lecture 14, Slide 15

16. Physics 212 Lecture 14, Slide 16 Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x Adding Magnetic Fields A) Left B) Right C) Up D) Down E) Zero x :13

17. Physics 212 Lecture 14, Slide 17 Force between current-carrying wires I towards us Conclusion: Currents in same direction_____________ I towards us Conclusion: Currents in opposite direction ____________ :16 Another I towards us  Another I away from us

18. Physics 212 Lecture 14, Slide 18

19. Physics 212 Lecture 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 Two Current Loops

20. Physics 212 Lecture 14, Slide 20Calculation 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? Conceptual Analysis y x. z I 1 =1A Front view Side view Strategic Analysis I 2 =1A 4cm 4cm y P 3cm :33

21. Physics 212 Lecture 14, Slide 21

22. Physics 212 Lecture 14, Slide 22