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3.1.3.      Gauss’ Law <CJ chap 18.9  >

3.1.3.1. Discussion

3.1.3.1.1.     Gauss’ law can be used to compute the electric field in symmetric cases.

3.1.3.1.2.     For a conductor:

3.1.3.1.3.     The electric field is zero everywhere inside a conductor thus conductors can be used to shield

3.1.3.1.4.     Any excess charge resides on the surface of the conductor

3.1.3.1.5.     On an irregular shaped conductor, charge accumulates where the radius of curvature is the smallest.

3.1.3.2. Mathematical

3.1.3.2.1.     Derivations from Gauss’ law

3.1.3.2.1.1. Plane:  E = s /(2e₀)              

3.1.3.2.1.2. Line charge: E= l/(2pe₀r)

3.1.3.2.1.3. Inside a parallel plate capacitor:  E = s /(e₀) and is uniform                 

3.1.3.2.1.4. E = s /e₀   = Also just outside a conductor

3.1.3.3. Advanced

3.1.3.3.1.     Gauss’ Law:

3.1.3.3.1.1. The electric flux F = E   ds  through a closed surface       F = q_inside /e₀

3.1.3.3.1.2. Thus E   ds  = q_inside /e₀

3.1.3.3.2.     Derive Gauss’ law from Coulomb’s