1 / 23

Physics 212 Lecture 14

Physics 212 Lecture 14. Biot-Savart Law. :05. Music. What is the answer to this question? B E A D C. Physics 212 Lecture 14. Right Hand Rule: Uses. 1. ANY CROSS PRODUCT. 2. VECTOR DESCRIPTION of ANY quantity that CURLS/ turns/circulates/…. Fingers: Circulating Quantity.

sowders
Download Presentation

Physics 212 Lecture 14

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Music • What is the answer to this question? • B • E • A • D • C Physics 212 Lecture 14

  3. Right Hand Rule: Uses 1. ANY CROSS PRODUCT 2. VECTOR DESCRIPTION of ANY quantity that CURLS/ turns/circulates/… Fingers: Circulating Quantity Thumb: Associated Vector + and by good fortune, the direction of the Magnetic Fieldaround a Current  Fingers: Magnetic Field Thumb: Current 06

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

  5. Direction: Thumb:on I Fingers:curl in direction of B B from infinite line of current Integratinggives result Magnitude: B Current I OUT r • r = distance from wire :07

  6. 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”? A) Left B) Right C) Up D) Down E) Zero :13

  7. Calculation . 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? y 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 :33

  8. Calculation . . . . . . • What is the direction of B at P produced by the top current I1? y y y y y z z z z z P P P P P (A) (B) (C) (D) (E) 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? y I1=1A 4cm 3cm x z P 4cm I2=1A Front view Side view :35

  9. Calculation . . . . . . y y y y y z z z z z P P P P P 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? y I1=1A 4cm 3cm x z P 4cm I2=1A Front view Side view • What is the direction of B at P produced by the bottom current I2? (A) (B) (C) (D) (E) :37

  10. Calculation . . . . . . y y y y y 90o z z z z P P P P (A) (B) (C) (D) 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? y I1=1A 4cm 3cm x z P 4cm I2=1A Front view Side view • What is the direction of B at P? z P :40

  11. Calculation . . • What is the magnitude of B at P produced by the top current I1? (m0 = 4p x 10-7 T-m/A) (A) 4.0 x 10-6T (B) 5.0 x 10-6T (C) 6.7 x 10-6T y r 4cm z 3cm 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? y I1=1A 4cm 3cm x z P 4cm I2=1A Front view Side view • What is r? • r = distance from wire axis to P :45

  12. Calculation . . • What is the magnitude of B at P? (m0 = 4p x 10-7 T-m/A) (A) 3.2 x 10-6T (B) 4.8 x 10-6T (C) 6.4 x 10-6T (D) 8.0 x 10-6T B1 q 5cm q q q B2 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? y I1=1A 4cm 3cm x z P 4cm Btop = 4 X 10-6 T I2=1A Front view Side view y 4cm z 3cm :49

  13. B • F On to magnetic FORCES On segments of wire, this gives: A long straight wire is carrying current from left to right. Two identical charges are moving with equal speed. Compare the magnitude of the force on charge a moving directly to the right, to the magnitude of the force on charge b moving up and to the right at the instant shown (i.e. same distance from the wire). v • v F (b) (a) r r I • |Fa |> |Fb| • |Fa |= |Fb| • |Fa |< |Fb| Same q, |v|, B andq (=90)! Forces are in different directions 28 :10

  14. B d F Another I towards us • B I towards us F d •  Another I away from us Force between current-carrying wires I towards us • Conclusion: Currents in same direction attract! Conclusion: Currents in opposite direction repel! :16

  15. Checkpoint 1 B X F 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 No torque about any axis 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 Uniform force at every segment of wire :18

  16. 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 WHY?? DRAW A SKETCH !! :21

  17. F into screen F out of screen Consider Force on Symmetric Segments! B I I Wire 2 r B r Wire 1 Net Force is Zero! :22

  18. Checkpoint 3b B i i F out of screen F into screen B 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

  19. Checkpoint 2 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 A B C D E :24

  20. Checkpoint 2 B1 B1 B2 X X X F2 F1 F1 B ~ 1/R B1 > B2 Fnet 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? Ftop + Fbottom =0 • 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 A B C D E :24

  21. B on axis from Current Loop :24

  22. What about Off-Axis ?? Biot-Savart Works, but need to do numerically See Simulation !! :24

  23. Two Current Loops 2) Look like bar magnets S S N N 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 ways to see this: • Like currents attract :30

More Related