- #1
Uku
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Homework Statement
Find a point on the line connecting two charges q_{1} and q_{1}
where the electric field strength is zero. These charges q_{1} and q_{1} at a distance of d.
NB - the charges can be of the same charge or different charge.
The Attempt at a Solution
I know the answer to be (say x is the distance):
x=\frac{\sqrt{q_{1}}}{\sqrt{q_{1}}\pm\sqrt{q_{2}}}d (1)
Right, for starters I assume that these charges are both positive? and I place a negative test charge to the right of the two charges, at a distance of x. This means that the test charge is at a distance d+x from the first charge.
Right, without revealing the in-between I reach a point where, by superposition
E_{1}-E_{2}=0
and dividing that by k
\frac{q_{1}}{(d+x)^{2}}-\frac{q_{2}}{x^{2}}=0
from where I reach the following by taking a square root of the above expression (by which I lose one solution?)
x=\frac{\sqrt{q_{2}}}{\sqrt{q_{1}}+\sqrt{q_{2}}}d
but that does not match up with the answer in the book. (1)
Especially the fact that q_{2} is in the top of the division, not q_{1}, the plus-minus part I don't mind.
