Physics 2102 Lecture 15. Physics 2102

Transcription

1 Physics 212 Jonathan Dowling Physics 212 Lectue 15 iot-savat Law Jean-aptiste iot ( ) Felix Savat ( )

2 What Ae We Going to Lean? A Road Map Electic chage Electic foce on othe electic chages Electic field, and electic potential Moving electic chages : cuent Electonic cicuit components: batteies, esistos, capacitos Electic cuents Magnetic field Magnetic foce on moving chages Time-vaying magnetic field Electic Field Moe cicuit components: inductos. Electomagnetic waves light waves Geometical Optics (light ays). Physical optics (light waves)

3 Electic Cuent: A Souce of Magnetic Field Obsevation: an electic cuent ceates a magnetic field Simple expeiment: hold a cuentcaying wie nea a compass needle! I Wie with cuent INTO page

4 Yet Anothe Right Hand Rule! Point you thumb along the diection of the cuent in a staight wie The magnetic field ceated by the cuent consists of cicula loops diected along you culed finges. i The magnetic field gets weake with distance. You can apply this to ANY staight wie (even a small diffeential element!) What if you have a cuved wie? eak into small elements. Diection of??? i

5 Supeposition Magnetic fields (like electic fields) can be supeimposed -- just do a vecto sum of fom diffeent souces The figue shows fou wies located at the 4 cones of a squae. They cay equal cuents in diections indicated What is the diection of at the cente of the squae? OUT IN OUT IN

6 When we computed the electic field due to chages we used Coulomb s law. If one had a lage iegula object, one boke it into infinitesimal pieces and computed, de 1 4!" dq ˆ 2 iot-savat Law Which we wite as, de dq 4!" If you wish to compute the magnetic field due to a cuent in a wie, you use the law of iot and Savat.

7 Jean-aptiste iot ( ) The iot-savat Law Quantitative ule fo computing the magnetic field fom any electic cuent Choose a diffeential element of wie of length dl and caying a cuent i The field d fom this element at a point located by the vecto is given by the iot-savat Law 4πx1-7 Tm/A (pemeability constant) dl idl! d 4 " Compae with i de dq 4!" Felix Savat ( )

8 iot-savat Law An infinitely long staight wie caies a cuent i. Detemine the magnetic field geneated at a point located at a pependicula distance R fom the wie. Choose an element ds as shown iot-savat Law: d points INTO the page Integate ove all such elements ids! d 4 " d 4" ids( sin! ) " i ds( sin$ )! 4% #"

9 Field of a Staight Wie ids! d 4 " d 4" ids( sin! ) sin! R / ( s R ) 1/ 2 " i ds( sin$ )! 4% #" " i Rds! / 4$ #" + R 2 " ( 2 2 s ) i Rds! 2# R ( 2 2 s + ) ' ir s % 2( 2 %& R R ( 2 2 s + ) / 2 1/ 2 $ " "#! i 2! R

10 Example : A Pactical Matte A powe line caies a cuent of 5 A. What is the magnetic field in a house located 1 m away fom the powe line? i 2! R " 7 (4! x1 T. m / A)(5A) 2! (1m) 1 T!! Recall that the eath s magnetic field is ~1 4 T 1 T

11 iot-savat Law A cicula ac of wie of adius R caies a cuent i. What is the magnetic field at the cente of the loop? ids! d 4 " idsr ird! d 2 4" R 4" R id! i# $ 4" R 4" R Diection of?? Not anothe ight hand ule?! TWO ight hand ules!: If you thumb points along the CURRENT, you finges will point in the same diection as the FIELD. If you cul ou finges aound diection of CURRENT, you thumb points along FIELD! i

12 Foces between wies Magnetic field due to wie 1 whee the wie 2 is, L I 1 I 2 1 I 1 2! a F Foce on wie 2 due to this field, F L I LI1I 2! a 2 a

13 Summay Magnetic fields exet foces on moving chages: The foce is pependicula to the field and the velocity. A cuent loop is a magnetic dipole moment. Unifom magnetic fields exet toques on dipole moments. Electic cuents poduce magnetic fields: To compute magnetic fields poduced by cuents, use iot- Savat s law fo each element of cuent, and then integate. Staight cuents poduce cicula magnetic field lines, with amplitude i/2π (use ight hand ule fo diection). Cicula cuents poduce a magnetic field at the cente (given by anothe ight hand ule) equal to iφ/4π Wies cuying cuents poduce foces on each othe: paallel cuents attact, antipaallel cuents epel.