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Homework Statement
A -1.0 nC charge and a 1.0 nC charge are separated by 10.0 cm.
a) At what position(s) is the electric field due to the two charges zero?
b) At what position(s) is the electric potential due to the two charges zero?
c) Draw a graph showing the zero electric field and zero potential positions.
Homework Equations
[itex]E = \frac{kq}{r^2}[/itex]
[itex]V= \frac{kq_1}{r_1} + \frac{kq_2}{r_2}[/itex]
The Attempt at a Solution
I was able to figure out the answer for part a, the position in which the electric field is zero between the two charges, and got an answer of 5cm doing the following steps:
[tex]
\frac{kq_1}{r_1^2} = \frac{kq_2}{r_2^2}\\
\frac{q_1}{r_1^2} = \frac{q_2}{r_2^2}\\
\frac{q_1}{r_1^2} = \frac{q_2}{(10-r_1)^2}\\
\frac{1}{r_1^2} = \frac{1}{(10-r_1)^2}\\
r_1^2 = (10-r_1)^2\\
r_1^2 = r_1^2 - 20r_1 + 100\\
-20r_1 + 100 = 0\\
-20r_1 = -100\\
r_1 = 5[/tex]
For part b, I got the same answer using a similar approach:
[tex]
V = \frac{kq_1}{r_1} + \frac{kq_2}{r_2}\\
V = \frac{q_1}{r_1} + \frac{q_2}{r_2}\\
V = \frac{q_1}{r_1} + \frac{q_2}{10-r_1}\\
0 = \frac{-1}{r_1} + \frac{1}{10-r_1}\\
\frac{1}{r_1} = \frac{1}{10-r_1}\\
r_1 = 10-r_1\\
r_1 = 10 - r_1\\
2r_1 = 10\\
r_1 = 5\\[/tex]
Now for my problem. In part b, I'm not sure if I used the correct formula. I did some research on this and in a couple of the example, instead of changing ##r_2## to ##10-r_1##, they just replaced ##r_1## with ##10## which ends up giving an answer of -10cm. The other examples did exactly what I did, including my class notes.
Assuming the method I used is correct, to answer part c, I would create a point, ##Q_1##, and draw two circle around it at equal distance from each other. The inner circle will be 5cm from ##Q_1## and will be labeled as "zero electric field and zero potential". The outer circle will be 10cm from ##Q_1## and I would place another point along said circle and label it ##Q_2##.
Example (Not photoshopped to scale):
I guess what I'm asking is, did I mess up somewhere because it seems too convenient that part a and b are the same and I'm not entirely sure if the graph is correct. Since it's asking for position(s), and 5cm is just the distance from a point, it should be in any direction from the point, and not locked into one specific location, thus the circle. Am I right to assume this?