How do we know the point of 0 electric field is on the axis?

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The discussion centers on the assumption that the point of zero electric field between two charges lies along the axis connecting them. This is justified by the requirement that for two vectors to sum to zero, they must be equal in magnitude and opposite in direction, which occurs only along the line connecting the charges. Points off this axis cannot achieve a zero electric field because the vectors from each charge would not be antiparallel. The conversation highlights a lack of resources explaining this concept in textbooks or online. Understanding this principle is crucial for solving related physics problems effectively.
laser
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Homework Statement
E=0
Relevant Equations
Electric field is a vector
In many homework problems I've encountered, they all seem to assume the electric field = 0 point is along the axis of the two charges. Intuitively it kind of makes sense, but I'm looking for a solid justification for it. In other words, why can't it be off the axis of the two charges? When setting up the problem, everyone seems to just assume it is on the axis.

Couldn't find any information about this in the book/online. Thanks!
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Draw the electric field at points outside the líne that joins q1 and q2
 
The only way to add two vectors to get zero is if they have equal magnitudes and are antiparallel.
 
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… and the only places where they are antiparallel is where the two charges and the point of zero field all lie on the same line.
 
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Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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