1. For each of the problems, does the solution make sense to you? What does it mean? Are the units correct? The numerical value of the solution is of limited value in this regard. It is much more important to consider the solution stated in terms of the symbols used to represent values of the data. (This is a perfect opportunity to correct errors.)

2. Compare the solutions for Problems 1 and 2, and consider the statement that "Given the same total charge, the solution for Problem 2 should be intermediate between the solution for a disk (Problem 1) and the solution for a ring of charge of radius RR." Justify or contradict this statement. For what value of σ 0 σ 0 would the total charge on the disk in Problem 2 be the same as the total charge on the disk in Problem 1? Can you suggest a form for the surface charge density that would produce an electric field intermediate between that of a point charge and the disk?

3. Why do you suppose that electrical engineers usually design structures that are flat disks or cylinders? (Look at any circuit board in a radio, DVD player, or computer for examples.)

4. In Problem 4b, the overall charge of the distribution is positive, yet the electric field at the field point specified in the problem was inward toward the origin instead of outward away from the charge distribution. Explain in a qualitative way (that is, without doing any calculations) why this is possible, and true in this case.

5. What connections can you find between these introductory prolems to more "real world" problems in chemistry, engineering, medicine, or biology? Do you expect that "real world" problems will require less mathematics than were needed in this workshop, or more?

1. What did you learn from participation in this exercise? What was new to you? What requirements found in performing the exercise were surprises to you?

2. If the mathematics is a problem for you, what do you plan to do about increasing your mathematics skills? (One useful course is to return to your calculus and/or pre-calculus textbook and work a lot of the end-of-chapter problems.)

3. How do the problems addressed in this module relate to medicine, biology, engineering, mathematics and chemistry (choose the area most important to you)? Can the problems addressed here be generalized to problems in fields other than physics?

4. What are advantages gained by using vector notation as opposed to writing separate equations for each component? Are there any disadvantages to use of vector notation? If you think so, what are they? In this, we have used two slightly different vector notations. In one, we write vectors as sums involving unit vectors, as in A ⇀ = a x ⁢ x ^ + a y ⁢ y ^ + a z ⁢ z ^ A ⇀ = a x ⁢ x ^ + a y ⁢ y ^ + a z ⁢ z ^ . In the other, we write vectors as ordered lists, as in A ⇀ = { a x , a y , a z } A ⇀ = { a x , a y , a z }. The two notations are connected by the definitions x ^ := { 1 , 0 , 0 } x ^ := {1,0,0}, y ^ := { 0 , 1 , 0 } y ^ := {0,1,0} and z ^ := { 0 , 0 , 1 } z ^ := {0,0,1}. Do you have a preference for one of these styles over the other? Why? Some textbooks use { i ^ , j ^ , k ^ } = { x ^ , y ^ , z ^ } { i ^ , j ^ , k ^ } = { x ^ , y ^ , z ^ }. Does this make any difference at all?