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Unformatted text preview: midterm 03 KIM, JI Due: Apr 3 2008, 11:00 pm 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 charge-pair: 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 plate-capacitor: 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 loop-arrow entering terminal for loop-arrow-parallel 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...
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