Electricity & Magnetism Lecture 14

Transcription

1 Electricit & Magnetism Lecture 14 Toda s Concept: Biot- Savart Law Electricit & Magne=sm Lecture 14, Slide 1

2 Your comments are important to somebod lease explain how wires exert torque on each other and how poten=al energ of a single wire in a magne=c field is determined (What is the equilibrium posi=on of a wire in a magne=c field) I think I dislocated m wrist while tring to appl the right hand rule Shouldn't all current in a wire flow on the outside surface, and therefore the magne=c field inside it be ero? AUer all the suffering I went through with Gauss Law, this topic seems eas What is the trick with the ver last checkpoint ques=on?

3 What is it? Biot-Savart Law: Fundamental law for determining the direc=on and magnitude of the magne=c field due to an element of current It is named for Jean-Baptiste Biot and Felix Savart who discovered this relationship in 1820 We can use this law to calculate the magne=c field produced b ANY current distribu=on BUT Eas anal=c calcula=ons are possible onl for a few distribu=ons: Text Axis of Current Loop Infinite Straight Wire lan for Toda: Mainl use the results of these calcula=ons! GOOD NEWS: Remember Gauss Law? Allowed us to calculate E for smmetrical charge distribu=ons NEXT TIME: Introduce Ampère s Law Allows us to calculate B for smmetrical current distribu=ons Electricit & Magne=sm Lecture 14, Slide 2

4 B from Infinite Line of Current Magnitude: Integra=ng gives result r = distance from wire B r Current I OUT µ 0 = T m/a Direc=on: Thumb: on I Fingers: curl in direc=on of B Electricit & Magne=sm Lecture 14, Slide 3

5 Currents + Charges A long straight wire is carring current from leu to right Two iden=cal charges are moving with equal speed Compare the magnitude of the force on charge a moving directl to the right, to the magnitude of the force on charge b moving up and to the right at the instant shown (ie same distance from the wire) (a) r v (b) r v I A) F a > F b B) F a = F b C) F a < F b Electricit & Magne=sm Lecture 14, Slide 4

6 Adding Magnetic Fields Two long wires carr opposite current x What is the direc=on of the magne=c field above, and midwa between the two wires carring current at the point marked? A) LeU B) Right C) Up D) Down E) Zero Electricit & Magne=sm Lecture 14, Slide 5

7 Force Between Current-Carring Wires I towards d B us F Another I towards us F 12 = I 2 L µ 0 2 d I 1 Conclusion: Currents in same direc=on airact! I towards B us d F Another I awa from us Conclusion: Currents in opposite direc=on repel! Electricit & Magne=sm Lecture 14, Slide 6

8 Checkoint 2 & 4 What is the direc=on 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 direc=on of the torque on wire 2 due to wire 1? A) Up B) Down C) Into Screen D) Out of screen E) Zero Electricit & Magne=sm Lecture 14, Slide 7

9 Checkoint 7 What is the direc=on of the force on wire 2 due to wire 1? A) Up B) Down C) Into Screen D) Out of screen E) Zero Electricit & Magne=sm Lecture 14, Slide 8

10 Consider Force on Smmetric Segments B I F out of screen I F into screen B r r Net Force is Zero! What about torque? Electricit & Magne=sm Lecture 14, Slide 9

11 Checkoint 9 What is the net torque on wire 2 due to wire 1? 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 Electricit & Magne=sm Lecture 14, Slide 10

12 Consider Force on Smmetric Segments τ B I F out of screen I F into screen B r Text r What about torque? Electricit & Magne=sm Lecture 14, Slide 9

13 B on axis from Current Loop I Resul&ng B Field Current in Wire Electricit & Magne=sm Lecture 14, Slide 12

14 Two Current Loops Two iden=cal loops are hung next to each other Current flows in the same direc=on in both The loops will: A) Airact each other B) Repel each other Electricit & Magne=sm Lecture 14, Slide 13

15 Right Hand Rule Review 1 ANY CROSS RODUCT 2 Direc=on of Magne=c Moment Fingers: Current in Loop Thumb: Magne=c Moment 3 Direc=on of Magne=c Field from Wire Fingers: Magne=c Field Thumb: Current Electricit & Magne=sm Lecture 14, Slide 14

16 Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? I 1 = 1A I 2 = 1A x 3cm Front view Side view Conceptual Analsis Each wire creates a magne=c field at B from infinite wire: B = m 0 I / 2πr Total magne=c field at obtained from superposi=on Strategic Analsis Calculate B at from each wire separatel Total B = vector sum of individual B fields Electricit & Magne=sm Lecture 14, Slide 15

17 Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? I 1 = 1A I 2 = 1A x 3cm Front view Side view What is the direc=on of B at produced b the top current I 1? A B C D E Electricit & Magne=sm Lecture 14, Slide 16

18 What is the direc=on of B at produced b the boiom current I 2? Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? Front view I 1 = 1A I 2 = 1A x 3cm Side view A B C D E Electricit & Magne=sm Lecture 14, Slide 17

19 Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? I 1 = 1A I 2 = 1A x 3cm What is the direc=on of B at? Front view Side view A B C D Electricit & Magne=sm Lecture 14, Slide 18

20 Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? What is the magnitude of B at produced b the top current I 1? (µ 0 = 4π x 10 7 T m/a) A) 40 x 10 6 T B) 50 x 10 6 T C) 67 x 10 6 T Front view I 1 = 1A I 2 = 1A x 3cm Side view Electricit & Magne=sm Lecture 14, Slide 19

21 Calculation Two parallel horiontal wires are located in the ver=cal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direc=ons shown What is the B field at point? B top = 4 x 10 6 T Front view I 1 = 1A I 2 = 1A x 3cm What is the magnitude of B at? (µ 0 = 4π x 10-7 T - m/a) A) 32 x 10 6 T B) 48 x 10 6 T C) 64 x 10 6 T D) 80 x 10 6 T Electricit & Magne=sm Lecture 14, Slide 20