Electricity & Magnetism Lecture 14

Transcription

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

2 The order of events Toda we will do Unit 26 S 1 Wednesda will do Unit 26 S2 Frida will do Unit 27 S1 to learn Oscilloscope Monda will do Unit 26 S3

3 Your comments are important to somebod Could ou summarie all the right hand rules? 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 magnec field inside it be ero? Is it intenonal for homework from Biot-Savart Law to Farada's Law to be due on the same da? That's a lot of homeworkthree is usuall barel tolerable (TT_TT) pls hev merc Are there an formulas that are general and can be used for an tpe of problem, or are there specific formulas for specific situaons? I found the lecture for the hsics 212 online and it explained things a lot beyer than the prelecture I actuall understand how to use the right hand rule now

4 This lecture seemed eas, but mabe I don't know what I don't know

5 What is it? Biot-Savart Law: Fundamental law for determining the direcon and magnitude of the magnec 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 magnec field produced b ANY current distribuon BUT Eas analc calculaons are possible onl for a few distribuons: Text Axis of Current Loop Infinite Straight Wire lan for Toda: Mainl use the results of these calculaons! GOOD NEWS: Remember Gauss Law? Allowed us to calculate E for smmetrical charge distribuons NEXT TIME: Introduce Ampère s Law Allows us to calculate B for smmetrical current distribuons Electricit & Magne/sm Lecture 14, Slide 2

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

7 Currents + Charges A long straight wire is carring current from led 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

8 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) Leb B) Right C) Up D) Down E) Zero Electricit & Magne/sm Lecture 14, Slide 5

9 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 direcon ayract! I towards B us d F Another I awa from us Conclusion: Currents in opposite direcon repel! Electricit & Magne/sm Lecture 14, Slide 6

10 Checkoint 2 & 4 What is the direcon 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 direcon 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

11 Checkoint 7 What is the direcon 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

12 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

13 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 Text Electricit & Magne/sm Lecture 14, Slide 10

14 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

15 B on axis from Current Loop I Resulng B Field Current in Wire Electricit & Magne/sm Lecture 14, Slide 12

16 Two Current Loops Two idencal loops are hung next to each other Current flows in the same direcon in both The loops will: A) A`ract each other B) Repel each other Electricit & Magne/sm Lecture 14, Slide 13

17 Right Hand Rule Review 1 ANY CROSS RODUCT 2 Direcon of Magnec Moment Fingers: Current in Loop Thumb: Magne/c Moment 3 Direcon of Magnec Field from Wire Fingers: Magne/c Field Thumb: Current Electricit & Magne/sm Lecture 14, Slide 14

18 Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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 magnec field at B from infinite wire: B = µ 0 I / 2πr Total magnec field at obtained from superposion Strategic Analsis Calculate B at from each wire separatel Total B = vector sum of individual B fields Electricit & Magne/sm Lecture 14, Slide 15

19 Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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

20 What is the direc/on of B at produced b the bo`om current I 2? Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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

21 Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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

22 Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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) Text 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 µ 0 2 = T m/a Electricit & Magne/sm Lecture 14, Slide 19

23 Calculation Two parallel horiontal wires are located in the vercal (x,) plane as shown Each wire carries a current of I = 1A flowing in the direcons 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 B total = B x1 + B x2 = 2 3! T = T 5 Electricit & Magne/sm Lecture 14, Slide 20