+ Objective: Given charge distribution; find

+ line charge:
surface charge:
volume charge:
steps: coordinates, (dl, ds or dv), , and
apply
Example 3.7: Potential for a line charge

+ Electric flux (Sect. 3.4)
-- electric flux density ( );

+ Gauss's law -- from Maxwell's equation: flux on a Gaussian surface
Q -- free charge enclosed by the surface

-- volume density ( ) of free charge

+ Step in apply Gauss's law to find field:
Pick a Gaussian surface such that
Find net free charges Q enclosed by the Gaussian surface where may be found from integration of , or .
= Q / area of Gaussian surface;
Example 3.8: Electric field from a point charge
Example 3.9: Electric field from a line charge

Here is a sphere with a charge of 1 nC uniformly distributed through it. The radius of the sphere is 100 mm, and the electric field's magnitude is measured in V/m. (Adopted from http://www.rpi.edu/dept/phys/Dept2/phys2/activities/gauss/examples.html)

+ Recap: Gauss's law -- for a Gaussian surface ; Q -- net free charge enclosed
Pick a Gaussian surface such that
Find net free charges Q enclosed by the surface
= Q / area of Gaussian surface;
Note: outward pointing normal.
2nd Maxwell's equation:
Given , find or

+ Free charges exist in free space and conductors. Both media have permittivity

+ Properties of conductors (Sect. 3.6.1):
Inside a conductor,
perpendicular to surface of a conductor and ,
i.e. tangential component and normal component

+ Properties of dielectric (insulator) (Sect 3.6.2): Have bounded surface charge and bounded volume charge created by electric dipoles of molecules
Volume density of dipole moment give polarization
,
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HW #15	Due 4/3/07

1. A circular disk of radius a is uniformly charged with . If the disk lies on the z=0 plane with its axis along the z-axis, (a) show that at point , and (b) use the formula in (a) to find the field due to an infinite sheet of charge on the z=0 plane. (Note: read example 3.4 on the web)
2. i) Find potentials at point P in Problem 3.3 (p. 143) for the charge ratios in (a) and (b) assuming and ii) find the electric field due to the potential .
3. Find the potential at for the charge system in problem 1.

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Last Modified: March 24, 2007
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