webassign(.)net/yf/22-30.gif
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.
A. To determine the signs of the three charges, we need to analyze the behavior of the electric field lines shown in the image.
From the image, we can observe that the electric field lines radiate outward from each charge. This indicates that the charges are positive, as positive charges create electric fields that extend outward. Negative charges, on the other hand, would generate electric fields that terminate on the charges.
Therefore, based on the behavior of the field lines in the image, we can conclude that all three charges are positive.
B. The points at which the magnitude of the electric field is the smallest can be identified by examining the spacing between the electric field lines. The closer the lines are to each other, the stronger the electric field, and vice versa.
In the image, the electric field lines are closest together at the center point between the three charges. Hence, this is the point where the magnitude of the electric field is the smallest.
C. The net electric field at the center point is small due to the combination of the individual electric fields produced by each point charge.
When the charges are aligned along the vertical axis, the electric fields they generate add up or cancel out at different points. At the center point, the electric fields produced by the charges are in opposite directions. Since the charges have the same magnitude, their electric fields cancel each other out, resulting in a small net electric field at this point.
Overall, the combined effect of the individual point charges produces a small net electric field at the center point, where the electric field lines are closely packed together.
To answer these questions, we need to analyze the given image of electric field lines due to three point charges. Let's go through each question one by one and explain how to approach solving them.
A. What are the signs of the three charges? Explain reasoning.
To determine the signs of the charges, we need to examine the behavior of the electric field lines. Remember that electric field lines start at positive charges and end at negative charges. Looking at the image, we see that the electric field lines originate from the three charges and extend outward vertically.
Examine the direction of the electric field lines between any two adjacent charges. If the field lines between two charges point in opposite directions, it means that the charges have opposite signs since one is acting as the source of electric field and the other as the sink.
In this case, we observe that the electric field lines bend towards the middle charge. This indicates that the middle charge is negative, as the field lines are directed towards it. The charges on either side should be positive, since the field lines emanate away from them.
Therefore, the reasoning suggests that the signs of the three charges are as follows:
- The left charge is positive.
- The middle charge is negative.
- The right charge is positive.
B. At what points is the magnitude of the electric field the smallest? Explain reasoning.
To determine where the magnitude of the electric field is the smallest, we need to focus on regions where the electric field lines are closely spaced or concentrated.
By observing the image, you can see that the field lines are most concentrated near the middle charge, where they bend inwards. This is an indication of higher field strength. As we move away from the middle charge towards the positive charges on the sides, the field lines start spreading apart, indicating a decrease in field strength.
Therefore, the magnitude of the electric field is the smallest at points further away from the middle charge and closer to the positive charges on either side.
C. Explain how the field produced by each individual point charge combines to give a small net field at this point or points.
The net electric field at a given point due to multiple charges is obtained by vector addition of their individual electric fields. In this case, the point in question is the one where the field lines are closest, in the region between the positive charges.
The middle negative charge and the positive charges on either side produce electric fields that partially cancel each other out, resulting in a smaller net electric field.
This happens because the electric field lines originating from the positive charges are directed away from them while the field lines originating from the negative charge are directed towards it. Since the magnitudes of the charges are the same, these opposing field lines partially cancel out, resulting in a smaller net field in this region.
Therefore, the combination of the individual electric fields from the three charges leads to a small net electric field in the region between the positive charges.