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Gauss' Law problem types and hints

Gauss' Law problem types and hints - SUNY Geneseo...

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SUNY Geneseo, Department of Physics and Astronomy Physics 125: Analytical Physics II Types of Gauss’ Law Problems There are a limited number of Gauss’ Law problems, and certain types of equations that will always com up in each type. Notation: Below, I’ll always use r for the radius of the Gaussian surface, and use a for the radius of physical charged objects. It is rarely the case that you want r and a to be the same. Problem Type Charge densities likely to be involved Conductor with Cavity Always use a Gaussian surface that passes through “the meat” of the conductor (shape is unimportant), so that 0 enc surrounded inner surface 0 q Q Q ε = Φ = = + Likely to want to use charge conservation on the conductor: conductor outer surface inner surface Q Q Q = + Q , σ Spherical Symmetry Always use Gaussian surface (sphere with radius r ), so that ( ) 2 0 0 enc 4 E r q ε π ε = Φ = Likely to want to use some combination of the following to get q enc ( ) 2 4 q a σ π = 3 4 3 q a ρ π = Q , σ , ρ Cylindrical Symmetry (infinitely long)
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