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Unformatted text preview: midterm 01 – LIN, KEVIN – Due: Feb 14 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 N m 2 /C 2 ǫ = 1 4 π 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: 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: λ = Δ Q Δ x Area charge density: σ A = Δ Q Δ A Surface charge density: σ surf = Δ Q surf Δ A Volume charge density: ρ = Δ Q Δ V Electric flux and Gauss’ law Flux: ΔΦ = E Δ A ⊥ = vector E · ˆ n Δ A Gauss law: Outgoing Flux from S, Φ S = Q enclosed ǫ Steps: to obtain electric field –Inspect vector E pattern and construct S –Find Φ s = contintegraltext surface vector E · d vector A = Q encl ǫ , solve for vector E Spherical: Φ s = 4 π r 2 E Cylindrical: Φ s = 2 π r ℓE Pill box: Φ s = E Δ A , 1 side; = 2 E Δ A , 2 sides Conductor: vector E in = 0, E bardbl surf = 0, E ⊥ surf = σ surf ǫ Potential Potential energy: Δ U = q Δ 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:  Δ V  =  E Δ s bardbl  , Δ V = − vector E · Δ vectors , V B − V A = − integraltext B A vector E · dvectors E = − d V dr , E x = − Δ V Δ 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 = ǫ A d Energy: U = integraltext Q V dq = 1 2 Q 2 C , u = 1 2 ǫ E 2 Dielectrics: C = κC , U κ = 1 2 κ Q 2 C , u κ = 1 2 ǫ κE 2 κ Spherical capacitor: V = Q 4 π ǫ r 1 − Q 4 π ǫ r 2 Potential energy: U = − vector p · vector E Current and resistance Current: I = d Q dt = nq v d A Ohm’s law: V = I R , E = ρJ E = V ℓ , J = I A , R = ρℓ A Power: P = I V = V 2 R = I 2 R Thermal coefficient of ρ : α = Δ ρ ρ Δ T Motion of free electrons in an ideal conductor: aτ = v d → q E m τ = J n q → ρ = m n q 2 τ 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 Kirchhoff’s Rules –Label currents: i 1 ,i 2 ,i 3 ,......
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 Spring '08
 Turner
 Physics, Charge, Electrostatics, Force, Electric charge, charge density, Kevin –, Ub Ut Ub Ut Ub Ut Ub Ut Ub Ut Ub Ut Ub Ut Ub Ut Ub Ut Ub

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