Exam 1 Laundry List PH 316 Fall 2000 - Added items are in brown.

• set up an integral for E or V on the axis of a disc of radius R and uniform charge density sigma
• set up an integral for E or V on the axis of a cylinder of uniform charge density rho
• set up an integral for E or V at a point (x,y) from a line of uniform charge density

• Give the definition of curl in terms of circulation and area
• State Stokes' theorem, having to do with circulation and curl
• Give the definition of divergence in terms of flux and volume
• State Gauss' theorem, having to do with flux and divergence

• show that the gradient of 1/s is -s/s^3, where s is the magnitude of r-r'
• from V = integral k rho dv/s and E = integral k rho (-s/s^3) dv that E =- grad V

• Use Gauss's law and Gauss's theorem to show div E = rho/epsilon_0 [pp. 68-69]
• Use Gauss's law to find E given a symmetrical charge distribution [sect 2.2.3]
• State integral form of gauss's law, having to do with flux and charge
• State the 'point' form of Gauss's law, having to do with divergence

• From E = - grad V and Gauss's law, obtain poisson's equation:
  the laplacian of V = -rho/epsilon_o
• When rho =0 (no raw charges) we have laplace's equation, laplacian V = 0.

• Electric conductors
• Argue for zero electric field inside a static conductor
• Argue for curl E = 0 for any static electric field
• Use Gauss's law to show Esurface = 4 pi k sigma
• Argue for Esurface being perpendicular to the surface
• Argue for a 'local' electric field at the surface of 2 pi k sigma
• Be able to interpret electric potential values near a conductor so as to estimate the surface charge distribution in a flat region compared to near a sharp corner (as was done with some spreadsheet data).

• Laplace's equation
• the average of V over a spherical surface is V at the center of the sphere
• in 2-d, on a spreadsheet V at the center cell is the average of the four surrounding cells
• show that in rectangular coordinates in 2-d (x,y) when we separate variables, one coordinate (x or y) will have solutions which are sines and cosines, and the other coordinate (y or x) will have solutions which are exponentials.
• be ready to solve laplace's equation iteratively on a spreadsheet using the averaging property

• Be able to expand a function in terms of a binomial series, or a taylor series.