PHY303L Final - E& M Basic Physical Concepts Electric...

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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 ² = 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: ~ 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: 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 ⊥ = ~ E · ˆ n Δ A Gauss law: Outgoing Flux from S, Φ S = Q enclosed ² Steps: to obtain electric field –Inspect ~ E pattern and construct S –Find Φ s = H surface ~ E · d ~ A = Q encl ² , solve for ~ E Spherical: Φ s = 4 π r 2 E Cylindrical: Φ s = 2 π r ‘E Pill box: Φ s = E Δ A , 1 side; = 2 E Δ A , 2 sides Conductor: ~ E in = 0, E k surf = 0, E ⊥ surf = σ surf ² 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 charge-pair: U = k q 1 q 2 r 12 Potential difference: | Δ V | = | E Δ s k | , Δ V =- ~ E · Δ ~s , V B- V A =- R B A ~ E · d~s E =- d V dr , E x =- Δ V Δ 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 plate-capacitor: C = Q V = Q E d = ² A d Energy: U = R Q V dq = 1 2 Q 2 C , u = 1 2 ² E 2 Dielectrics: C = κC , U κ = 1 2 κ Q 2 C , u κ = 1 2 ² κE 2 κ Spherical capacitor: V = Q 4 π ² r 1- Q 4 π ² r 2 Potential energy: U =- ~ p · ~ E Current and resistance Current: I = d Q dt = nq v d A Ohm’s law: V = I R , E = ρJ E = V ‘ , J = I A , R = ρ‘ 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 ,... –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 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 μ = 4 π × 10- 7 T m / A Wire: B = μ i 2 π r Axis of loop: B = μ 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.

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PHY303L Final - E& M Basic Physical Concepts Electric...

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