Equations - Midterm 1 - Constants e 1.60 10 C k 9.0 109...

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Constants 19 10 60 . 1 × = e C 9 10 0 . 9 × = k N·m 2 /C 2 0 4 1 πε = 12 0 10 85 . 8 4 1 - × = k π ε C 2 /N·m 2 7 0 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 0 ε enc q A d E = > Spherical Symmetry , radius=R Outside: 2 0 4 r kQ r Q E = = πε , drops as 1/r 2 Inside (uniformly charged): 3 R kQr E = Inside (hollow): 0 = E > Line Symmetry , λ=Charge per unit length Outside: r E 0 2 πε λ = , drops 1/r Inside (hollow): 0 = E Gauss’s Law ( con’t) : > Plane Symmetry , σ =Charge per unit area Outside: 0 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 0 / 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 0 2 1 E u E ε = Total Electric Energy stored in field: = = 2 0 2 1 E dV u U E ε Capacitors , Capacitance= V Q C / = Parallel-plate Capacitors: d A C / 0 ε = Energy Stored in Cap.: 2 2 1 CV U = Capacitors in Parallel: 2 1 C C C + = > Capacitors in Parallel have same Voltage. Capacitors in Series: 2 1 1 1 1 C C C + = > Capacitors in Series have same Charge.
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