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Physics Cheat Sheet (Final Exam for 2nd part of physics)

Physics Cheat Sheet (Final Exam for 2nd part of physics) -...

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Physics Formulas for Final Exam (May ’96) Gravitational Acceleration: a GM r g = 2 Gravitational Potential Energy U GMm r = - Circular Orbit: K U = 2 Energy U K = = - 2 Energy in Planetary Motion When a planet or satellite with mass m moves in a circular orbit with radius r , its potential energy U and kinetic energy K are given by U GMm r = - K GMm r = 2 The total mechanical energy E = K + U is E GMm a = - 2 in which the radius r has been replaced with the semimajor axis a to indicate that this expression for total energy is also valid for more general elliptical orbits. The Electric Field h E F q o = E q r o = 4 2 πε (point charge) 2 E p z o = 2 3 πε (electric dipole) 2 E qz z R o = + 4 2 2 3 2 πε c h / (charged ring) 2 E z z R o = - + F H G I K J σ ε 2 1 2 2 (charged disk) p qd = (dipole moment) τ = × p E (torque dipole) U p E = - (dipole pot. eng.) The Electric Field & Gauss’ Law E F q = Φ = v A (Flux) 2 2 E dA q o = z ε E r o = λ π ε 2 (line of charge) q L = λ E o = σ ε 2 (sheet of charge) q A = σ E o = σ ε (conducting surface) E Q r o = 4 2 πε (spherical shell) Electric Potential Energy U U U W f i if = - = - U W f = - V V V f i W q if o = - = - (potential difference defined) V V E ds f i i f - = z (Finding V from E) V E ds i f = - z V q r o = 4 πε (Potential Due to Point charges) V q r o = ρ θ πε cos 4 2 (Potential Due to an Electric Dipole) U W q q r o = = 1 2 4 πε
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