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).
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