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Equations - Midterm 1

Equations - Midterm 1 - 60 1 × = e C 9 10 9 × = k N·m...

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Unformatted text preview: Constants 19 10 60 . 1 × = e C 9 10 . 9 × = k N·m 2 /C 2 4 1 πε = 12 10 85 . 8 4 1- × ≈ = k π ε C 2 /N·m 2 7 10 4- × = π μ N/A 2 or T·m/A Coulomb’s Law , r r q kq F ˆ 2 2 1 12 = Electric Fields, E q F = Field of Point Charge: r r kq q F E test ˆ 2 = = Continuous Charge Distributions: ∫ ⋅ = r r dq k E ˆ 2 Acceleration of Particle: E m q a ) / ( = E of ∞ line/wire = r k ÷ λ 2 , λ = charge per unit length, drops as 1/r Dipoles , from – to +, drops as 1/r 3 Dipole moment: qd p = Torque: θ τ sin ⋅ ⋅ = × = E p E p Work=PE= E p U ⋅- = Electric Flux A E A d E ⋅ = ⋅ = Φ ∫ Gauss’ Law ε enc q A d E = ⋅ ∫ > Spherical Symmetry , radius=R Outside: 2 4 r kQ r Q E = = πε , drops as 1/r 2 Inside (uniformly charged): 3 R kQr E = Inside (hollow): = E > Line Symmetry , λ=Charge per unit length Outside: r E 2 πε λ = , drops 1/r Inside (hollow): = E Gauss’s Law ( con’t) : > Plane Symmetry , σ =Charge per unit area Outside: 2 ε σ = E > Electric field=0 inside conductor in electrostatic equilibrium, charges on surface > Any net charges reside on conductor’s surface > Electric field at the surface is perpendicular and / ε σ = E Electric Potential PE Difference: ∫ ⋅- = ∆ B A AB r d F U Electric Potential Diff.: ∫ ⋅- = ∆ B A AB r d E V AB AB U V q ∆ = ∆ ⋅ Potential of Point-Charge: r kq V r = ∞ P. of Continuous Charge Dis.: ∫ ⋅ = r dq k V Dipole Potential: 2 cos r kp V θ = Equipotential: dx dV E x- = Energy Density: 2 2 1 E u E ε = Total Electric Energy stored in field: ∫ ∫ = ⋅ = 2 2 1 E dV u U E ε Capacitors , Capacitance= V Q C / = Parallel-plate Capacitors: d A C / ε = Energy Stored in Cap.: 2 2 1 CV U = Capacitors in Parallel: 2 1 C C C + = > Capacitors in Parallel have same Voltage....
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Equations - Midterm 1 - 60 1 × = e C 9 10 9 × = k N·m...

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