Two charges located along x. Find all values?

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The problem involves two charges, one at "-a" and another at "+3a," with the goal of determining the unknown charge's value based on the net electric field at the origin. The equations used indicate that the electric field contributions from both charges must equal either 2Ke(Q/a²) or -2Ke(Q/a²) at the origin. The signs of the charges are crucial in determining the direction of the electric field; the first charge is assumed to point towards the origin while the second charge points away. The calculations yield two possible values for the unknown charge: -9Q if the net field is positive, and 27Q if it is negative. Thus, the unknown charge is confirmed to be positive.
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Homework Statement


The first one has charge Q is at "-a" from origin the second is at "+3a" which is an unknown charge.What are the values for unknown charge if at the origin the net electric field they produce with magnitude 2Ke(Q/a2)

Homework Equations


Ke (Q/a2)i - Ke(q/9a2)=2Ke(Q/a2)i
if charge is negative
or
if the charge is positive
Ke (Q/a2)i - Ke(q/9a2)=-2Ke(Q/a2)i

The Attempt at a Solution


The question is how to choose signs for equation.
Attempt:
Assuming charge one is pointed towards the origin along x-axis so the sign will be "+i" and the second charge is pointed towards the origin in the negative x direction so tthe sign will be "-i".
Two possible values are at the origin: "+" or "-" 2Ke(Q/a2) .
If you choose "+" at the origin the answer will be -9Q. And for case chosen "-" sign in the origin, the answer will be 27Q so the particle has positive charge.
I wondering if this is the explanation?
 
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Correct.
 
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