Midterm preparation:

The midterm is scheduled for Wednesday, October 27. There are many ways to prepare.  What I recommend is to focus on working and redoing homework problems.   If you do homework problems in the style expected for the midterm, that is really good preparation; I think that will help you when you get to the midterm.   The following approach is useful for many problems:

1.  draw a picture
2.  define a coordinate system (sketch that on your picture)
3.  write down the relevant equations in terms of both given (known) and unknown quantities defined in a manner consistent with your picture and coordinate system 
4.  using the equations to solve for your unknown quantity or quantities (variables) in terms of known (given) quantities
5. graph your result, if requested

 All these parts are important.  True, on most HW problems they do not ask you to graph anything, but  graphing is important and will be present on the midterm to some degree.
        You will also be given problems in which you start with the graph (of some quantity as a function of a variable, like x)  and are then ask questions about that graph (including creating another graph from the graph you are given).  For example you may be given a graph of V(x) (Volts), as a function of x,  and then asked to graph the  x-component of the electric field (also as a function of x).

Here are some practice problems that you can use for preparation in addition to using some of the HW problems:

practice problem #1:
Suppose there are two charges which are .2 m apart. One has a charge, q,  of 1 C; the other has a charge of -1 C.

a)  sketch a picture of the two charges and mark the point halfway in between the two.
What is the electric field at that point? (What would the electric field at that point be if both charges were positive?)

b)  define and sketch a coordinate system and then calculate the electric field as a function of the distance from that center point, p,  along the direction perpendicular to the line connecting the two charges.  how many non-zero components does the electric field have?

c)   Graph each nonzero component of the electric field (as a function of the distance from that center point, p,  along the direction perpendicular to the line connecting the two charges).  put titles, such as x-component of electric field as a function of y,  labels, and scales on your graph and graph axes, respectively. Make it clear what your coordinate system is! Use picture and words! The correspondence between your variables, coordinate system and picture should be made very clear. You will get more credit if you make things clear; you will get less if you leaves things ambiguous. [The graders will grade by addition, from zero, not by subtraction for errors!]

practice problem #2:
Suppose there are two charges which are .2 m apart. One has a charge, q,  of 1 C; the other has a charge of -1 C. (This is similar, but asks about potential.) 

a)  sketch a picture of the two charges and mark the point halfway in between the two.
What is the electric potential at that point?

b)  define and sketch a coordinate system and then calculate the electric potential as a function of the distance from that center point, p,  along the direction perpendicular to the line connecting the two charges.  Is this easier or more difficult than the preceding problem? Why?

c)   Graph the electric potential (as a function of the distance from that center point, p,  along the direction perpendicular to the line connecting the two charges). Why is this more difficult/less difficult than problem 1?
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(Do the same two problems for 2 positive charges (+1 C each). How does that change your results and graphs.)

3. Suppose you are given an electric potential,: V(x)= Ax^2

b) graph V(x)

a) what are the units of A?

c) calculate and graph the x-component of the electric field as a function of x.

d) If a positively charged particle, the charge of +2 coulombs were placed at x = 2 meters, what force would it experience?

e) Does that force depend on x?  what would it be at x=4 m?