Where Electric Field Strength + Potential are Zero?

[karine]

Homework Statement

draw equipotential lines and electric field lines for the following arrangements of charges:
a) +4 at (3,5)
b) +4 at (3,5) and +4 at (6,5)
c) +4 at (3,5) and -4 at (6,5)
d) +5 at (3,5) and -2 at (6,5)
e) +4 at (3,4), (7,4), and (7,7)
f) +4 at (3,4) and (7,4) and -4 at (3,7) and (7,7)
h) +4 at (3,4),(7,4), and (5,8)

#1: find the places in the arrangements from a-f where electric field strength is zero. show your work. State the x,y coordinate where the electric field strength is zero
#2: find the places in each arrangement where the electric potential is zero. show your work.

Homework Equations

e = \frac{k|q|}{r^{2}}
V = \frac{kq}{r}

The Attempt at a Solution

First of all, my teacher directed me to this applet thing to see what the equipotential and electric field lines would look like, which is this:
http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html
so I tried to plot the points and I saved each one as a picture. With this: "draw equipotential lines and electric field lines", show I use the pictures or draw them completely new on separate graph paper?
for #1 for arrangement B, I figured because of the distance the place would be in the middle of the two charges, so at (4.5,6), but I have no idea how I could prove this with any of the equations I've learned. If I use e = k |q| / r^2, and sub in e for 0 and try to find r, I get 189 736.66 :S
I also don't understand how using e = k |q| / r^2 incorporates the fact that there are two charges.
I realize that's not a lot of work done on my own, but I really don't understand what I'm supposed to be doing at all.
This is at a grade 12 level.

 

[vindarmagnus]

The thing you're missing is that the maxwell equations are linear and can be super-positioned. That is, if you know the field distribution for one charge, and then you place another charge somewhere, you just add the two fields together. That's why we can integrate charges spread out on a circle for example. So the equations you have describe the field around one charge, where r is the distance from that specific charge. So if you want to know the total field, just add them together (but remember to keep track of which r belongs to which charge).

/M