Exam3_EquationSheet

Exam3_EquationSheet - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2010 Exam Three Equation Sheet Force Law: ( ) q ext ext q = + × F E v B r r r r Faraday’s law d d d dt = − ∫∫ E s B a r r r r ± Gauss’s Law: inside closedsurface / o d Q ε = ∫∫ E A r r ± Gauss’s Law for Magnetism: 0 closed surface d = ∫∫ B A r r ± Ampere’s Law 0 o o d d d d dt μ μ ε = + ∫∫ ∫∫ B s J a E a r r r r r r ± Electric Potential Difference: b b a a V V V d Δ = ≡ − E s r r V = −∇ E r r Potential Energy: U q V Δ = Δ Capacitance: V Q C Δ = 2 2 1 1 2 2 Q U C V C = = Δ Inductance: B / L N I = Φ back / LdI dt ε = − 2 1 2 L U LI = Energy Density Stored in Fields: 2 1 0 2 E u E ε = ; 2 1 0 2 / B u B μ = Current Density and Current: open surface
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