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Unformatted text preview: 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 N m 2 /C 2 = 1 4 k = 8 . 854187817 10 12 C 2 /N m 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: ~ E = ~ F q Point charge:  E  = k  Q  r 2 , ~ E = ~ E 1 + ~ E 2 + Field patterns: point charge, dipole, k 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 = ~ E n A Gauss law: Outgoing Flux from S, S = Q enclosed Steps: to obtain electric field Inspect ~ E pattern and construct S Find s = H surface ~ E d ~ A = Q encl , solve for ~ 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: ~ E in = 0, E k 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 k  , V = ~ E ~s , V B V A = R B A ~ E d~s E = d V dr , E x = V x fl fl fl 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 = R 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 = ~ p ~ 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 d q dt + R d i dt = i c + R d i dt = 0 Discharge: 0 = V c Ri = q c + R d q dt , i c + R d i dt = 0 Magnetic field and magnetic force = 4 10 7 T m / A Wire: B = i 2 r Axis of loop: B = a 2 i 2 ( a 2 + x 2 ) 3 / 2 Magnetic force: ~ F M = i ~ ~ B q~v...
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This note was uploaded on 01/20/2010 for the course PHY 1 taught by Professor Erskine during the Spring '10 term at University of Texas at Austin.
 Spring '10
 ERSKINE
 Physics, Charge, Force

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