GAUSS'S LAW STUDY GUIDE

AP LEARNING TARGETS

TERMS:

  • Test Charge: A mathematical construct-- a charge that does not exert any influence on surrounding particles but IS influenced by other electric fields.
  • conductor - materials where electrons can roam
  • insulator - materials that keep their electrons close to home
  • coulomb - a unit of electrical charge (see below)

CONSTANTS:

  • e-mass = 9.1 x 10-31 kg
  • charge of an electron = 1.60 x 10-19 coulombs (C)
  • ke = 8.987 x 109 Nm2/C2
  • ke = 1/4πεo

FORMULISTICS:

      Electrical Force: Fe = (keq1q2)/r2

      Electrical Field:

        • E = Fe / qo where qo  = a positive test charge

        • E= (keq)/r2

      Gauss's Law (for an object enclosing 1 or more charged particles)

      • Φ = E A dA or EAcosθ dA where θ is the angle between the electrical field line vector and the area vector

      • Φ = qin/εo : the electric flux through an ENTIRE gaussian surface is equal to the algebraic sum of the charges INSIDE the surface divided by the permitivity of free space

      Generally: the more symetric the surface area of the gaussian surface the more accurate is this formula.

CONCEPTS:
  • What is an electric field?
  • What are electric field lines?
  • What is a test charge? What are the unique properties of a test charge and why are they important to keep in mind?
  • What is a gaussian surface and why do we care?
  • What is an area vector?
  • What is the effect of presence or absence of charges inside a gaussian surface on any analysis of electric flux in and out of that surface?
  • Why do we use the "dot" product of the area vector with the electric field vector when calculating electric flux?
  • What is the effect of surface area symetry on any analysis of electric flux in and out of a gaussian surface?
  • What is the effect of a uniform electric field on any anlysis of electric flux in and out of a gaussian surface?
  • Mr Chase tells us (quite correctly by the by) that we can ALWAYS use:

Φ = qin/εo

to calculate the electric flux through a gaussian surface. What are the limitations to this approach and when does it work best?