Electric field direction when solving system?

[Kavorka]

In a problem when you are placing a third charge so that E=0 at the origin, I know how you are suppose to sum the electric field of each point charge at the origin and set it to 0 in order to solve for the distance of the third charge. I have a slight confusion, however, on how to set the signs of each E with respect to the origin. To use a simple 1-D example to show my confusion:

A point charge of +5 micro C is located on the x-axis at x = -3 cm, and a second point charge of -8 micro C is located on the x-axis at x = +4 cm. Where should a third charge of 6 micro C be placed so that the electric field at the origin is zero?

The answer to the problem sets the direction of E on the -8 and +6 charges as -i, and +i on the +5 charge. I'm not sure why this is. Aren't we just pretending there's a positive test charge at the origin and looking at the direction each charge pushes it? If that is so, the 5 micro C chare would push it right so +i, the -8 micro C charge would pull it right so +i, and the +6 micro C charge, deduced to be places left of x = -3cm, would push it to the right so +i. Even if you reverse the direction sign for the negative charge it doesn't match. I'm just confused as to assigning these vector directions, not as to how to solve the rest of the problem.

 

[Konoha]

If I got the question right, the +5 micro C charge is at x=-3 cm, so the electric field in the origin resulting should be in +i direction. (which is what you said) and the -8 micro C charge is at x=+4, so its electric field in the origin also is in the direction of +i. (as you said we imagine there is a positive test charge in the origin and see what is the direction of force on it, and I guess this is what you believe yourself) so now the electric field resulting from these two charges points to right (+i), hence we have to place the third charge somewhere to have an electric field pointing to left (-i) at the origin in order to cancel out these fields. since the third charge is positive the only way we can place it to have an electric field pointing to left in the origin is if it was located at x>0. and then you have to solve the rest of problem to find the location of the third charge.

 

[Konoha]

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