(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a point on the line connecting two charges [tex]q_{1}[/tex] and [tex]q_{1}[/tex]

where the electric field strength is zero. These charges [tex]q_{1}[/tex] and [tex]q_{1}[/tex] at a distance of [tex]d[/tex].

NB - the charges can be of the same charge or different charge.

3. The attempt at a solution

I know the answer to be (say x is the distance):

[tex]x=\frac{\sqrt{q_{1}}}{\sqrt{q_{1}}\pm\sqrt{q_{2}}}d[/tex] (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 [tex]x[/tex]. This means that the test charge is at a distance [tex]d+x[/tex] from the first charge.

Right, without revealing the in-between I reach a point where, by superposition

[tex]E_{1}-E_{2}=0[/tex]

and dividing that by k

[tex]\frac{q_{1}}{(d+x)^{2}}-\frac{q_{2}}{x^{2}}=0[/tex]

from where I reach the following by taking a square root of the above expression (by which I lose one solution?)

[tex]x=\frac{\sqrt{q_{2}}}{\sqrt{q_{1}}+\sqrt{q_{2}}}d[/tex]

but that does not match up with the answer in the book. (1)

Especially the fact that [tex]q_{2}[/tex] is in the top of the division, not [tex]q_{1}[/tex], the plus-minus part I don't mind.

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# Homework Help: Electric field - point of zero field

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