PHYS 212, Honors Section – Review Material


Chapter 24: Gauss' Law

  • General concept: The flux of a constant vector field v through a flat surface of area A is

Φ = (v cosθ) A = v · A .

(Recall the concept of flow rate through a surface for a fluid.) 

  • Electric field flux: For a constant field through a flat surface, ΦE = (E cosθ) A = E · A. It can be interpreted as (proportional to) the number of field lines crossing the surface. For a non-constant field and/or a non-flat surface, apply the equation to each infinitesimal surface element and integrate,

ΦE = E · dA .

  • Gauss' law: Concept of Gaussian surface; The electric flux through a closed Gaussian surface is

ΦE = qin/ε0.

  • Charged conductors: Inside a conductor, the electric field is always zero in electrostatic equilibrium (conduction charges are not moving). Any excess charge on a conductor will be found entirely on its surface. What happens when there are cavities. Electric field at the surface of a conductor: It has to be perpendicular to the surface, and its magnitude is E = σ/ε0.
       
  • Applications of Gauss' law: Be able to apply it to situations with charged lines, planes, and volumes.
     
  • Results: For a large non-conducting sheet, E = σ/2ε0 on both sides; Outside a conducting plate, E = σ/ε0; Between two plates with opposite-sign charges, E = σ/ε0. (Recall the distinctions in the meanings of σ).

Note: You are not required to know the topics and equations inside square brackets.

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