This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: final 01 SAENZ, LORENZO Due: May 10 2008, noon 1 E & M  Basic Physical Concepts Electric force and electric field Electric force between 2 point charges:  F  = k  q 1   q 2  r 2 k = 8 . 987551787 10 9 Nm 2 /C 2 = 1 4 k = 8 . 854187817 10 12 C 2 /Nm 2 q p = q e = 1 . 60217733(49) 10 19 C m p = 1 . 672623(10) 10 27 kg m e = 9 . 1093897(54) 10 31 kg Electric field: vector E = vector F q Point charge:  E  = k  Q  r 2 , vector E = vector E 1 + vector E 2 + Field patterns: point charge, dipole, bardbl plates, rod, spheres, cylinders, ... Charge distributions: Linear charge density: = Q x Area charge density: A = Q A Surface charge density: surf = Q surf A Volume charge density: = Q V Electric flux and Gauss law Flux: = E A = vector E n A Gauss law: Outgoing Flux from S, S = Q enclosed Steps: to obtain electric field Inspect vector E pattern and construct S Find s = contintegraltext surface vector E d vector A = Q encl , solve for vector E Spherical: s = 4 r 2 E Cylindrical: s = 2 r E Pill box: s = E A , 1 side; = 2 E A , 2 sides Conductor: vector E in = 0, E bardbl surf = 0, E surf = surf Potential Potential energy: U = q V 1 eV 1 . 6 10 19 J Positive charge moves from high V to low V Point charge: V = k Q r V = V 1 + V 2 = ... Energy of a chargepair: U = k q 1 q 2 r 12 Potential difference:  V  =  E s bardbl  , V = vector E vectors , V B V A = integraltext B A vector E dvectors E = d V dr , E x = V x vextendsingle vextendsingle vextendsingle fix y,z = V x , etc. Capacitances Q = C V Series: V = Q C eq = Q C 1 + Q C 2 + Q C 3 + , Q = Q i Parallel: Q = C eq V = C 1 V + C 2 V + , V = V i Parallel platecapacitor: C = Q V = Q E d = A d Energy: U = integraltext Q V dq = 1 2 Q 2 C , u = 1 2 E 2 Dielectrics: C = C , U = 1 2 Q 2 C , u = 1 2 E 2 Spherical capacitor: V = Q 4 r 1 Q 4 r 2 Potential energy: U = vector p vector E Current and resistance Current: I = d Q dt = nq v d A Ohms law: V = I R , E = J E = V , J = I A , R = A Power: P = I V = V 2 R = I 2 R Thermal coefficient of : = T Motion of free electrons in an ideal conductor: a = v d q E m = J n q = m n q 2 Direct current circuits V = I R Series: V = I R eq = I R 1 + I R 2 + I R 3 + , I = I i Parallel: I = V R eq = V R 1 + V R 2 + V R 3 + , V = V i Steps: in application of Kirchhoffs Rules Label currents: i 1 ,i 2 ,i 3 ,... Node equations: i in = i out Loop equations: ( E ) + ( iR )=0 Natural: + for looparrow entering terminal for looparrowparallel to current flow RC circuit: if d y dt + 1 R C y = 0, y = y exp( t R C ) Charging: E V c Ri = 0, 1 c...
View Full
Document
 Spring '08
 Turner

Click to edit the document details