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

• AnonBae
In summary, the test charge at point A has no significant effect on the electric field at points B and C.
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?)

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.

#### Attachments

• Charge and rod broken up.PNG
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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.

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

rude man said:
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.

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence a charged object has on other charged objects within its vicinity. It is a vector field, meaning it has both magnitude and direction, and is created by the presence of electric charges.

## 2. What is a negative test charge?

A negative test charge is a hypothetical point charge with a negative charge that is used to measure the strength and direction of an electric field. It is typically much smaller than the other charged objects in the system and does not significantly affect the electric field.

## 3. How is the electric field calculated for a semicircular rod?

The electric field at any point due to a semicircular rod can be calculated using Coulomb's law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges. The direction of the electric field can be determined using the right-hand rule.

## 4. What factors affect the strength of the electric field acting on a negative test charge due to a semicircular rod?

The strength of the electric field acting on a negative test charge due to a semicircular rod depends on the magnitude of the charge on the rod, the distance between the negative test charge and the rod, and the shape of the rod. The electric field is stronger when the charge on the rod is larger and when the negative test charge is closer to the rod.

## 5. How does the direction of the semicircular rod affect the electric field acting on a negative test charge?

The direction of the semicircular rod does not affect the strength of the electric field acting on a negative test charge, but it does determine the direction of the electric field. The electric field lines always point away from the positive charge and towards the negative charge, so the direction of the semicircular rod will determine the direction of the electric field at any given point.

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