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The image above shows some of electric field lines due to 3 poin charges along the vertical axis. All 3 charges have the same magnitude. A. What are the signs of the 3 charges? Explain reasoning. B. At what points is the magnitude of the electric filed the smalles? Explain reasoning. C. Explain how the fielsd produced by each individual point charge combine to give a small net field at this point or points.
E points away from positive charges. Magnitude ought to be indiated by the spacing: narrower spacing, Higher E.
To answer these questions, we will need to analyze the image provided and understand the behavior of electric field lines due to point charges.
A. Determining the signs of the three charges:
From the image, we can observe that the electric field lines are radially directed away from the charges. By convention, electric field lines are drawn away from positively charged objects and towards negatively charged objects.
To determine the signs of the charges:
- Look at the direction of the electric field lines in the image.
- If the electric field lines are pointing away, the corresponding charge should be positive.
- If the electric field lines are pointing towards, the corresponding charge should be negative.
By examining the image, we can see that two of the charges have electric field lines pointing away from them, while one has electric field lines pointing towards it. Therefore, we can conclude:
- Two charges have positive signs.
- One charge has a negative sign.
B. Finding points with the smallest magnitude of the electric field:
The magnitude of the electric field decreases as we move away from the charges. Thus, the points with the smallest magnitude of the electric field will be farthest from the charges.
In the given image, the points with the smallest magnitude of the electric field are:
- The points located at the midpoint between the positive charges.
- The point located at the midpoint between the positive and negative charges.
These points are the furthest away from any of the charges, resulting in a smaller combined electric field magnitude.
C. Explaining the net field produced at these points:
When the electric fields due to multiple point charges combine at a particular point, their effects can either add up constructively or cancel out destructively.
At the points mentioned in part B, the net field produced by each individual point charge combines to give a small net field due to constructive interference.
- The positive charges contribute to the net field by adding their individual electric fields together.
- The negative charge contributes to the net field by producing an electric field in the opposite direction.
As the distances between the charges increase, and because the charges have the same magnitude, the magnitude of the electric fields produced by the positive charges becomes smaller. At the same time, the contribution from the negative charge remains constant.
The combination of smaller positive charge contributions and a constant negative charge contribution leads to a smaller net electric field at these specific points or range of points.