Inductance: Self and Mutual Inductance, Energy Storage, and Circuits, Study notes of Physics

Download Inductance: Self and Mutual Inductance, Energy Storage, and Circuits and more Study notes Physics in PDF only on Docsity! P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce In d u c ta n c e • S e lf i n d u c ta n c e – B a s ic d e fi n it io n – R L c ir c u it , tu rn o n – U n it s • E n e rg y i n B -f ie ld • S o le n o id • L o n g W ir e • C o a x – F ro m B a n d Φ – F ro m m o v e m e n t o f c u rr e n t e le m e n ts – F ro m f ie ld e n e rg y • R L c ir c u it , tu rn o ff . P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce S e lf i n d u c ta n c e
1 = - „ F „ t = - L I. F = ŸB ÿ„ A , B = m 0 4 p Ÿ „ s är` r2 I F = Im 0 4 p Ÿ Ÿ 1 r2 H„ s â r̀ Lÿ„ A M I = L I L = m 0 4 p Ÿ Ÿ 1 r2 H„ s â r̀ Lÿ„ A P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce E n e rg y i n B „ U „ t = P = IV = I L „ I „ t fl U B = 1 2 L I2 E n e rg y s to re d i n i n d u c to r U ~ L I2 ~ 1 L HL IL2 ~ A 2 L B 2 ~ A 2 m 0 l B 2 ~ l3 1 m 0 B 2 fl u B ª U V ~ 1 m 0 B 2 E n e rg y d e n s it y i n B L I = F ~ B A u s e P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce In d u c ta n c e o f s o le n o id B = m 0 N l I F = F 1 N = B A N = m 0 A l N 2 I \ L = m 0 A l N 2 U = 1 2 L I2 = 1 2 m 0 A l N 2 I 2 = 1 2 lA m 0 Im 0 N I l M2 = 1 2 V m 0 B 2 fl u B = 1 2 m 0 B 2 u E = 1 2 e 0 E 2 re c a ll P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce L o n g w ir e U = 1 2 L I2 = 1 2 1 m 0 Ÿ B 2 „ V L = 1 m 0 I 2 Ÿ B 2 „ V = l m 0 I 2 H m 0 I 2 p L2 Ÿ 2 p r r2 „ r \ L l = m 0 2 p ln Ir m ax r m in M P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce C o a x -I II : U s e l o n g w ir e f o rm u la ( fr o m B 2 ) r m ax r m in = b a L l = m 0 2 p ln Jr m ax r m in N= m 0 2 p ln Ib a M U l = 1 2 L l I 2 = 1 2 m 0 2 p ln Ib a M I 2 • T h re e t e c h n iq u e s f o r fi n d in g e n e rg y a n d in d u c ta n c e p e r le n g th . – F ro m f lu x – F ro m f o rc e – F ro m B 2 • A ll g iv e s a m e r e s u lt P h y s 2 0 8 , F a ll 2 0 0 6 N o v . 1 0 , 2 0 0 6 In d u ct a n ce D is s ip a ti o n o f fi e ld e n e rg y I = - t „ I „ t , t = L êR I = I 0 e - têt P R = I2 R = I 02 e - 2 tê t R U = ŸP „ t = I 02 t 2 R = 1 2 L I 02 F ie ld e n e rg y i s d is s ip a te d i n r e s is to r.