Set 1 Due Monday September 8, 2003

• Text 2-11, p. 62
• Text, 2-3 p. 61 (sigma is charge/area, the surface charge density)
• Find the x and y components of the electric field at (0.0, 0.05) m due to a +1 microcoulomb charge at the origin and a -2 microcoulomb charge at (0.04,0.0)m.

• Add two more electric field lines to the field line spreadsheet starter spreadsheet. This makes a plot with four field lines on it.
• Add in the presence of a third charge, so the field lines are for three charges.
• prob 2-16, p. 62
• prob 2-17, p. 63
• The two spreadsheet probs may be due on Friday 9/12 if people are having trouble with them.

•  2-29
•  2-36
• a) 3-13    b) 3-14
• a) 3-23    b) 3-24

• 5-1
• 5-7
• 5-11
• Reflection coefficient for E in the plane of incidence (algebra and plot from 0 to 90 degrees)

• Reflection coefficient for E perpendicular to the plane of incidence (algebra and plot from 0 to 90 degrees)

• 1. Text 6-13
• 2. Text 6-17

1. An electrostatic precipitator in a smokestack has a slender wire highly charged which ionizes the air around it and sends a shower of electrons which strike crud particles in the stack exhaust gases and cause them to be collected at the outer surface of the smokestack. Assume it takes 1.5E7 V/m to ionize the air, so this must be the electric field at the surface of the central wire. Take the smokestack to be cylindrical with a radius of 1.50 m, and the central wire to have a radius of 1.00 cm. In the calculations to follow, treat the wire as if it were infinite.
a) Find the surface charge density in C/m^2 on the wire.
b) Say whether the surface charge density is positive or negative
c) Calculate the potential difference between the central wire and the grounded cylinder on the outside of the stack.  Is the potential at the central wire positive or negative?

2. On p. 51 it is claimed that no stable equilibrium can exist due to static charges by themselves. On p. 65 there is a sketch of 8 identical charges at the corners of a cube. You might think the 8 charges would trap a positive charge at the center by pushing it back if it moved away from the center.

Let the x-axis be parallel to one edge of the cube, and the origin be at the center of the cube. Calculate the potential V(x) from x=0 to x=a. This goes from the center of the cube to the middle of one face, as is shown Figure 2.36, p. 65. Take the 8 charges to each be 1 microcoulomb, and just add the potentials from each of the 8 charges along the x-axis. It is claimed that if we put a positive charge at the origin, it would not be stable there. Your calculation should support this claim. Does it? [The potential energy of a charge q is qV. Should the potential energy be a maximum or a minimum for stability?]

3. Text problem 6-31, p. 162.   Let the boundary between hemispherical shells be in the x-y plane. You must integrate over one hemisphere in spherical polar coordinates to obtain the total force in the z-direction. This should give you an answer twice as high has the text answer. [Please do not quote the text about two charges separated by R sqrt(2); this has no value whatever and will get you zero credit unless you fully carry out the calculation.]  The reason for the extra factor of 2 is that the electric field at any point on the surface of a conducting sphere or shell is half due to that little section (acting like an infinite plane) and half due to all the other charges on the sphere.
 

1. Text 7-4
2. Text 7-12. You must supply the full set of reasoning, like we did in class for 7-11.

1.. Text 7-16. You must use the dipole field and integrate from the Earth's radius out over all space.
Take m = 8.8E22 A/m^2

Due Thursday November 13, 2003

1. (7) Work out, showing all your work, the two image charges needed where a charge Q is located in one half-infinite dielectric medium near a plane boundary with another half-infinite dielectric medium. Please make your arguments clear.[ See handout/worksheet.]