Physics 212 Lecture 14 BiotSavart Law 05 Physics

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

Biot-Savart Law: 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: Axis of Current Loop Infinite Straight Wire : 05 Physics 212 Lecture 14, Slide 2

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

B from infinite line of current Magnitude: B Current I OUT r • r = distance from wire Direction: Thumb: Fingers: : 07 on I curl in direction of B Physics 212 Lecture 14, Slide 4

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). (a) v F r v B • (b) r • F I a) |Fa |> |Fb| b) |Fa |= |Fb| c) |Fa |< |Fb| Same q, |v|, B and q (=90) Forces are in different directions 28 : 10 Physics 212 Lecture 14, Slide 5

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 : 13 B) Right C) Up D) Down E) Zero Physics 212 Lecture 14, Slide 6

Force between current-carrying wires I 1 d • F B • I 2 Conclusion: Currents in same direction attract. I 1 • d B F I 2 Conclusion: Currents in opposite direction repel. : 16 Physics 212 Lecture 14, Slide 7

Checkpoint 1 X B 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 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 : 18 Physics 212 Lecture 14, Slide 8

Checkpoint 3 a What is the direction of the force on wire 2 due to wire 1? A) Up : 21 B) Down C) Into Screen D) Out of screen E) Zero Physics 212 Lecture 14, Slide 9

Consider Force on Symmetric Segments! B I F out of screen r F into screen r Net Force is Zero! : 22 Physics 212 Lecture 14, Slide 10

Checkpoint 3 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 B i i B : 24 F out of screen F into screen Physics 212 Lecture 14, Slide 11

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? : 24 A. The forces are in opposite directions A The net forces are the same B. B C. 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 D. E There is no net force on the loop E. Physics 212 Lecture 14, Slide 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? Ftop + Fbottom =0 B 2 B 1 X X F 1 B ~ 1/R F 2 B 1 X F 1 B 1 > B 2 Fnet : 24 A. The forces are in opposite directions A The net forces are the same B. B C. 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 D. E There is no net force on the loop E. Physics 212 Lecture 14, Slide 13

B on axis from Current Loop : 24 Physics 212 Lecture 14, Slide 14

What about Off-Axis ? ? Biot-Savart works, but need to do numerically See Simulation !! : 24 Physics 212 Lecture 14, Slide 15

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

Two Current Loops 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: 1) Like currents attract 2) Look like bar magnets N : 30 S N S Physics 212 Lecture 14, Slide 17

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 Physics 212 Lecture 14, Slide 18

Calculation Two parallel horizontal wires are located in the vertical (x, y) plane as shown. Each wire carries a current of I =1 A flowing in the directions shown. y y I 1=1 A . 4 cm What is the B field at point P? x 4 cm 3 cm z I 2=1 A Front view Side view • What is the direction of B at P produced by the top current I 1? y y y . . . z P (A) : 35 z P (B) z P (C) P z P (D) z P (E) Physics 212 Lecture 14, Slide 19

Calculation Two parallel horizontal wires are located in the vertical (x, y) plane as shown. Each wire carries a current of I =1 A flowing in the directions shown. y y I 1=1 A . 4 cm What is the B field at point P? x 4 cm 3 cm z I 2=1 A Front view P Side view • What is the direction of B at P produced by the bottom current I 2? y y y . . . z P (A) : 37 z P (B) z P (C) z P (D) z P (E) Physics 212 Lecture 14, Slide 20

Calculation Two parallel horizontal wires are located in the vertical (x, y) plane as shown. Each wire carries a current of I =1 A flowing in the directions shown. y y I 1=1 A . 4 cm What is the B field at point P? x 4 cm z I 2=1 A Front view • What is the direction of B at P? y y y . . . z P (A) : 40 z P (B) z P Side view y . 90 o P (C) 3 cm z P (D) Physics 212 Lecture 14, Slide 21

Calculation Two parallel horizontal wires are located in the vertical (x, y) plane as shown. Each wire carries a current of I =1 A flowing in the directions shown. y y I 1=1 A . 4 cm What is the B field at point P? x 4 cm I 2=1 A Front view z 3 cm P Side view • What is the magnitude of B at P produced by the top current I 1? (m 0 = 4 p x 10 -7 T-m/A) (A) 4. 0 x 10 -6 T (B) 5. 0 x 10 -6 T (C) 6. 7 x 10 -6 T y . • What is r? – r = distance from wire axis to P 4 cm z : 45 r 3 cm Physics 212 Lecture 14, Slide 22

Calculation Two parallel horizontal wires are located in the vertical (x, y) plane as shown. Each wire carries a current of I =1 A flowing in the directions shown. What is the B field at point P? Btop = 4 X 10 -6 T y y I 1=1 A . 4 cm x 4 cm I 2=1 A Front view • What is the magnitude of B at P? (m 0 = 4 p x 10 -7 T-m/A) (A) 3. 2 x 10 -6 T (B) 4. 8 x 10 -6 T (C) 6. 4 x 10 -6 T z 3 cm P Side view (D) 8. 0 x 10 -6 T y . 4 cm 3 cm z q : 49 B 1 q 5 cm q q B 2 Physics 212 Lecture 14, Slide 23