FormulaSheet - Ben Sauerwine Qualifying Exam Study Sheet...

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Ben Sauerwine Qualifying Exam Study Sheet Mechanics (In this section, K indicates the kinetic energy of the system in terms of the variables and V indicates the potential.) Lagrangian: V K L = Hamiltonian: L p q V K H i i i = + = Above, the “conjugate momentum” of a coordinate is p = q L p & . Thus note that the equations of motion take a form like = q L p dt d which is essentially, “The time derivative of the momentum is the force.” Electricity and Magnetism Radiation pressure: c P Φ = . Maxwell’s Equations: Gauss: 0 ε ρ = E v v Gauss’s Law (magnetism): 0 0 = = H B v v r v Faraday’s Law: t B E = × v v v Ampere’s Law: t E J B + = × v v v v 0 0 0 μεμ The integral forms are related to these such that the cross products become loop integrals and the dot products become surface integrals. Note that in these may vary in matter.
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FormulaSheet - Ben Sauerwine Qualifying Exam Study Sheet...

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