Your Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows.

Transcription

1 You Comments lease explain the ight hand ule when thee ae two wies and ou ae ting to find the diection of the foce I am getting confused with all these ight hand ules So do ou have an age-old advice fo Unofficial? Afte Tuesdas lectue I felt like I undestood the toque stuff, but as soon as I stated going though these checkpoint questions I felt like I was in Memento and hadnt taken a single polaoid on Tuesda Can ou explain mathematicall, o at least qualitativel, the deivation/intuition of the iot- Savat Law? I feel the pe-lectue pesented it in a "tust us that this is tue" fashion duing the last couple lectues its been getting eall nois and had to hea, especiall fo the last couple ows The eason thee is such a discepanc between checkpoint scoes and i>clicke scoes is that thee is no incentive to do well on checkpoints, so most people simpl click andom answes and submit them Not that I'm encouaging ou to give points fo accuac on checkpoints Is it oka to sa that the field poduced b a loop will be paallel (o anti paallel) to mu vecto of the loop cause mu and want to be aligned? Also if E-fields and -fields ae elated b Loent boosts, ae mu naught and epsilon naught elated? M oommate and I ae having a competition to see who can get on the boad moe, since I didn't just click though the pelectue like SOMEONE, I think I deseve a shoutout Electicit & Magnetism Lectue 14, Slide 1

2 Ae we going to have to constantl deive the iot-savat law fo infinite wies with cuent (much like how we constantl used Gauss's Law to find the E-field fo vaious sphees/clindes), o is the (μ_o*i)/(2π) equation something we will use staight off the bat? hsics 212 Lectue 14 Toda s Concept: iot-savat Law d 0I d s ˆ 2 4 Electicit & Magnetism Lectue 14, Slide 2

3 F Right Hand Rule Review 1 ANY CROSS RODUCT qv F d F IL ˆ 0I d s Diection of Magnetic Moment Finges: Cuent in Loop Thumb: Magnetic Moment 3 Diection of Magnetic Field fom Wie Finges: Magnetic Field Thumb: Cuent Electicit & Magnetism Lectue 14, Slide 3

4 What is it? Fundamental law fo detemining the diection and magnitude of the magnetic field due to an element of cuent iot-savat Law: d 0I ds ˆ 2 4 We can use this law to calculate the magnetic field poduced b ANY cuent distibution UT Eas analtic calculations ae possible onl fo a few distibutions: Axis of Cuent Loop Infinite Staight Wie lan fo Toda: Mainl use the esults of these calculations! GOOD NEWS: Remembe Gauss Law? Allowed us to calculate E fo smmetical chage distibutions NEXT TIME: Intoduce Ampee s Law Allows us to calculate fo smmetical cuent distibutions Electicit & Magnetism Lectue 14, Slide 4

5 Magnitude: fom Infinite Line of Cuent Integating 0I Tm/ A distance fom wie d 4 0I d s ˆ 2 gives esult Cuent I OUT Diection: Thumb: on I Finges: cul in diection of Electicit & Magnetism Lectue 14, Slide 5

6 Cuents + Chages A long staight wie is caing cuent fom left to ight Two identical chages ae moving with equal speed Compae the magnitude of the foce on chage a moving diectl to the ight, to the magnitude of the foce on chage b moving up and to the ight at the instant shown (ie same distance fom the wie) A) F a > F b ) F a F b C) F a < F b (a) F v (b) Foces ae in diffeent diections v F F qv F qvsinq Same q, v, and q (90) I Electicit & Magnetism Lectue 14, Slide 6

7 Adding Magnetic Fields Two long wies ca opposite cuent x What is the diection of the magnetic field above, and midwa between the two wies caing cuent at the point maked X? A) Left ) Right C) Up D) Down E) Zeo x Electicit & Magnetism Lectue 14, Slide 7

8 Foce etween Cuent-Caing Wies I towads d F 12 I 2 L F 12 I 2 L o 2d I 1 us Anothe I towads us F Conclusion: Cuents in same diection attact! I towads us d F Anothe I awa fom us Conclusion: Cuents in opposite diection epel! Electicit & Magnetism Lectue 14, Slide 8

9 Checkoint 1 X F What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo 2 wies with same-diection cuents ae attacted What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unifom foce at eve segment of wie No toque about an axis If two wies ae caing cuent, and we ae asked to detemine the diection of net toque on one wie (Checkpoint Question 1 at 3), how do we detemine the diection of the vecto?

10 Checkoint 3 What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo WHY? DRAW ICTURE! Electicit & Magnetism Lectue 14, Slide 10

11 Conside Foce on Smmetic Segments I F out of sceen I F into sceen Net Foce is Zeo! Electicit & Magnetism Lectue 14, Slide 11

12 Checkoint 3b What is toque on wie 2, due to wie 1? Thee is a net foce on the ight side pointing into the sceen and a net foce on the left side pointing out of the sceen Using the ight hand ule, this means that the toque is pointing up What is the diection of the toque on wie 2 due to The wie wie 1? will t to align with wie 1 A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo I I F out of sceen F into sceen Electicit & Magnetism Lectue 14, Slide 12

13 Foce on cuent loop nea wie AA loop of wie with cuent flowing in a counteclockwise diection is located to the ight of a long wie with cuent flowing up As shown below What is the diection of the net foce on the loop? A) Up ) Down C) Left D) Right E) Zeo 1 X X 2 F 1 F 2 ~ 1/R 1 > 2 F 1 > F 2 Electicit & Magnetism Lectue 14, Slide 13

14 F top + F bottom 0 Checkoint 2 A cuent caing loop of width a and length b is placed nea a cuent caing wie How does the net foce on the loop compae to the net foce on a single wie segment of length a caing the same amount of cuent placed at the same distance fom the wie? 1 X X 2 X 1 F 1 F 2 ~ 1/R 1 > 2 F1 F net A The foces A ae in opposite diections The net C foces ae the same C The net D foce on the loop is geate than the net foce on the wie segment D The net E foce on the loop is smalle than the net foce on the wie segment E Thee is no net foce on the loop Electicit & Magnetism Lectue 14, Slide 14

15 on axis fom Cuent Loop I Resulting Field Cuent in Wie Electicit & Magnetism Lectue 14, Slide 15

16 Two Cuent Loops Two identical loops ae hung next to each othe Cuent flows in the same diection in both The loops will: A) Attact each othe ) Repel each othe Two was to see this: 1) Like cuents attact 2) Look like ba magnets N S N S Electicit & Magnetism Lectue 14, Slide 17

17 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A Font view Side view Conceptual Analsis Each wie ceates a magnetic field at fom infinite wie: m 0 I / 2p Total magnetic field at obtained fom supeposition Stategic Analsis Calculate at fom each wie sepaatel Total = vecto sum of individual fields Electicit & Magnetism Lectue 14, Slide 19

18 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A Font view Side view What is the diection of at poduced b the top cuent I 1? A C D E Electicit & Magnetism Lectue 14, Slide 20

19 What is the diection of at poduced b the bottom cuent I 2? Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? Font view I 1 1A I 2 1A x 3cm Side view A C D E Electicit & Magnetism Lectue 14, Slide 21

20 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A What is the diection of at? Font view Side view 90 o A C D Electicit & Magnetism Lectue 14, Slide 22

21 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? What is the magnitude of at poduced b the top cuent I 1? ( 0 4 x 10 7 Tm/A) A) 40 x 10 6 T ) 50 x 10 6 T C) 67 x 10 6 T What is? distance fom wie axis to 0I I ỵ Font view 3cm I 1 1A I 2 1A x 3cm Side view cm Electicit & Magnetism Lectue 14, Slide 23

22 top 4 x 10 6 T What is the magnitude of at? Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? Font view I 1 1A I 2 1A x 3cm ( 0 4 x 10-7 T m/a) A) 32 x 10 6 T ) 48 x 10 6 T C) 64 x 10 6 T D) 80 x 10 6 T ỵ q 5cm 3cm q q 1 q 2 1 x 1 cosq 2 x 2 cosq x cosq Electicit & Magnetism Lectue 14, Slide 24