Electric field acting on a negative test charge due to semicircular rod

[AnonBae]

Homework Statement

A thin semicircular rod is broken into two halves. The top half has a total charge +Q uniformly distributed along it, and the bottom half has a total charge -Q uniformly distributed along it. A negative test charge is placed at points A, B, and C.
*Image attached*
Consider the following incorrect statements made by three students:
1. "The test charge is negative, so it will reduce the electric field where it is placed."
2. "I disagree. The test charge is negative, so it will flip the direction of the electric field, but it won't change the magnitude."
3. "When the test charge is at point A, it contributes to the field at points B and C, but not at point A. Test charges don't affect the field where they are."

Explain why each studient is incorrect. (Hint: What assumptions are made about test charges?)

Homework Equations

ΣE = Fe/ q

The Attempt at a Solution

1. The electric field depends on the electric force and the charge the force is exerted on. The sign of the charge does not "reduce" the electric field but instead shifts the direction of the electric force when compared to a positive charge. Thus, the magnitude stays the same. (I really do not know how I justify its incorrectness).
2. The presence of the test charge may influence the distribution of the charges in the rod, but not so that it flips the direction of the electric field. The electric field spawns from the positive charges in the semicircular rod, and thus moving the negative test charge through the points does not necessarily flip the direction of the electric field but rather shifts the field lines.
3. The test charge does contribute to the field at point A, or where they are. Since the test charge is negative, the electric field lines will converge to the negative test charge.

I do not know if my explanations suffice. Any help is appreciated.

 

[haruspex]

Is the rod a conductor? If not, I would have said statement 3 is correct.
I get the feeling there are more parts to the question. It may clarify matters if you post all.

 

[rude man]

I think there's a much more basic answer, and it's hinted at above: "(Hint: What assumptions are made about test charges?)".

 

[haruspex]

I think there's a much more basic answer, and it's hinted at above: "(Hint: What assumptions are made about test charges?)".

I think I understand what you are saying, but I'm uneasy about saying it makes statement 3 wrong. You could qualify it thus:

"it contributes to the field at points B and C, but to a negligible extent"​

It is now unarguably correct, yet we have not withdrawn the statement that it does affect the field at B and C.