Physics II Equations Ch 21 Electric Charges F e k q1 q2 r2 0 8 85 10 12C 2 N m2 Ch 22 23 Electric Fields E F q0 E Ei i pE sin U p E pE cos E 2 k infinite plate 2 0 E dA E E 2 0 r 2 0 infinite line of charge uniform spherical shell Ch 24 Electric Potential V U q W q V on system K q V V Ed k 1 4 0 8 99 109 N m2 C 2 E kq r2 r Ed 2 kqd z3 p E E k dq r2 r E dA qen 0 E A uniform field E 2 0 infinite sheet W q U by system V E d s f i 1 eV 1 602 10 19 J V kq r point charge V k i qi ri V k dq r dV ds E s Ch 25 Capacitance q CV L C cylinder 2 k ln b a V s V i q p q i C p C i U C V 2 1 2 q 2 2 C E 0 E D 1 qD q 1 0 A d t 1 C 1 iavg q t J ne vd Ch 26 Current and Resistance V kp cos r2 dipole V disk 2 k a2 y 2 y E V C plates 0 A d q series constant 1 C s 1 C i V p constant W ext q 2 2 C u 0 E2 1 2 V D V 0 C D C 0 E d A q en 0 i dq dt V iR J E E 1 R L A Ch 27 Circuits E dW dq V 0 loop rule 1 R p n 1 R i i 1 i E R e t RC q C E e t RC discharging Ch 28 Magnetic Fields F qvB sin V H iB nqt T 2 m qB F iLB sin NiA n B 0 i 2 R coil NiABsin B sin Ch 29 Magnetic Field due to Current 1 P iV i2 R V 2 R i 0 juntion rule n R s Ri i 1 q C E 1 e t RC V E 1 e t RC r cyclotron F q v B mv qB qB 2 m f F i L B coil B 0 4 10 7 Tm A dB 0 4 ids sin r2 Barc 0 i 4 R B 0 ir 2 R2 r R B 0 2 z3 dipole E0 NBA L N i 0 n2 Al E L di dt Ls Li q Q cos t i I sin t Ch 30 Induction and Inductance B A BA cos B d A i e t L decaying current E R F q E v B Lorentz force Ch 31 Electromagnetic Oscillations and AC Current d B 0 4 id s r r2 B d s 0ien B 0 solenoid E N d dt P B2 L2 v2 R n turns length length 1 e t L i E R U L i2 1 2 E d s AdB dt 1 LC 1 RC I t U L i2 2 q2 2 C 2 R 2 L 2 V C I C X C V L I L X L I Em Z tan X L X C R V rms V 2 Pavg I 2 rms R E d A q en 0 B d A 0 E d s d B dt id 0 d E dt Ch 33 E M Waves c 3 00 108 m s Ch 32 Maxwell s Equations B d s 0ien 0 0 d E dt q t Q e Rt 2 L cos t V R I R R X C 1 C X L L I rms Erms I 2 E 2 ZX R2 X L X C 2 Gauss Law for electricity Gauss Law for magnetism Faraday s Law Ampere Maxwell Law S E B 1 0 p if all light reflected 2 U c tot reflection S EB 1 0 E 2 c 0 Erms Em 2 2 I c Pr n c v i r Ch 16 Waves I y x ym sin kx v f k T tot absorption I 1 c 0 2 Erms p U c Pr F A I c I I 0cos2 n1 sin 1 n 2sin 2 sin c n 1 n2 n2 n1 k 2 y x t ym sin kx t y x t t ymcos kx t 2 y x t t 2 2 ym sin kx t sin sin 2 cos y x t 2 ym cos 1 2 1 2 sin 1 2 y x t 2 ym cos t x nodes n 2 2 L n Ch 17 Waves II Sound L n 2 x n 1 2 2 n 2 Wave interference Standing wave Open pipe resonant standing wave L resonant standing wave P x t Pm sin kx t f L f nv 2 L n 4 nv 2 L v B L m 2 m L m 1 2 2m 1 1 2 I v 2 sm 2 Ch 34 Images 1 2 1 2 1 2 f r m h h i p Ch 35 Interference d sin m d sin m 1 2 Open pipe 1 open end 1 open end s x t sm cos kx t f f v vD v v S Fully constructive interference Fully constructive interference Fully destructive interference Fully destructive interference beat 1 2 10 dB log I I0 1 p 1 i 1 f n1 p n2 i n2 n 1 r Constructive Interference maxima Destructive Interference minima sin 2 d 2 m maxima 2m 1 minima L 0 2 n Constructive Interference Thin Film Destructive Interference Thin Film 2 I I m sin sin 1 22 Raleigh Criterion d d sin m X Ray Diffraction t t0 1 v2 c2 1 1 2 L L0 I 4 I0 cos2 2 n n 2 L m 1 2 n2 2 L m n2 Ch 36 Diffraction a sin m sin a hw Nd cos 2 d sin m Ch 37 Relativity t 0 2 D c v c t t 0 x x vt y y z z t t vx c 2 u v 1 u v v u c2 0 c E0 m c2 Lorentz Transformations f f 0 1 1 p m v 1 u 1 66 10 27 kg E E0 K mc2 K E m c2 Q M i c2 M f c2 M c2 K E m c2 mc2 mc2 m c2 1 pc 2 K 2 2 Km c2 E2 pc 2 mc2 2