Physics 212 Lecture 14

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

2. Biot-Savart Law: Axis of Current Loop Infinite Straight Wire 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: :05

3. Field at the center of a ring P points out of page for each

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

5. B • • F F Forces are in different directions Currents + Charges 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 (b) (a) r r I • |Fa |> |Fb| • |Fa |= |Fb| • |Fa |< |Fb| Same q, |v|, B andq (=90) 28 :10

6. Magnetic Fields obey superposition B x Two long wires carry equal and opposite currents 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. B d F I2 • B I1 F d •  I2 Force between current-carrying wires • I1 Conclusion: Currents in same direction attract. Conclusion: Currents in opposite direction repel. :16

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. B on axis from Current Loop :24

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

16. S N Magnetic field of a dipole moment Direction of B reverses from inside to outside. B gets weaker

17. 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

18. 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 06

19. 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

20. 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

21. 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

22. 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

23. 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