Question
Charges of +2 µC and +3 µC are 4 mm from each other. Raina’s group draws four diagrams trying to represent the electrical force between the charges.
4 pairs of charged particles. Each pair is labeled W, X, Y and Z respectively. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing left. A dot representing a charge on the right is labeled +3 microcoulombs with a vector pointing right. The pair is labeled W. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a longer vector pointing right. The pair is labeled X. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a vector pointing left. The pair is labeled Y. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a smaller vector pointing left. The pair is labeled Z.
Which diagram is correct?
W
X
Y
Z
4 pairs of charged particles. Each pair is labeled W, X, Y and Z respectively. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing left. A dot representing a charge on the right is labeled +3 microcoulombs with a vector pointing right. The pair is labeled W. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a longer vector pointing right. The pair is labeled X. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a vector pointing left. The pair is labeled Y. A dot representing a charge of a positive 2 microcoulombs is on the left with a vector pointing right. A dot representing a charge on the right is labeled +3 microcoulombs with a smaller vector pointing left. The pair is labeled Z.
Which diagram is correct?
W
X
Y
Z
Answers
Answered by
GPT-4o mini
To determine which diagram correctly represents the electrical force between the two charged particles (+2 µC and +3 µC), we need to consider the nature of like charges and the direction of the electric force:
1. Both charges are positive. According to Coulomb's law, like charges repel each other. Therefore, the electric force between these two charges will be directed away from each charge.
2. The charge of +2 µC will repel the charge of +3 µC to the right, resulting in a force vector pointing away from the +2 µC charge.
3. Similarly, the charge of +3 µC will repel the charge of +2 µC to the left, resulting in a force vector pointing away from the +3 µC charge.
Now, let’s analyze each option:
- **Diagram W**: Charge +2 µC has a vector pointing left (towards -∞), which is incorrect. Both vectors should point away from each other.
- **Diagram X**: Charge +2 µC has a vector pointing right (correct) and charge +3 µC has a longer vector pointing right. This suggests that the charge +3 µC is experiencing a stronger repulsive force, which is not how it should be represented; both repulsive forces should be equal in magnitude according to Coulomb's law, although the distances might be different.
- **Diagram Y**: Charge +2 µC has a vector pointing right (correct), but charge +3 µC has a vector pointing left (incorrect), since both should repel away from each other.
- **Diagram Z**: Charge +2 µC has a vector pointing right (correct) and charge +3 µC has a smaller vector pointing left. This, too, is incorrect as both should be pointing right.
So, none of the diagrams perfectly represent the situation correctly. However, the most consistent option that follows the rule of repulsion between like charges is Diagram X, but it still inaccurately suggests varying forces or magnitudes.
If you were to select the "least incorrect" representation based on the understanding of the forces involved, **Diagram X** would be the most appropriate choice, but it's important to note that it is not entirely correct. For strict accuracy, all the diagrams need to be revised to show two arrows pointing directly away from each charge.
1. Both charges are positive. According to Coulomb's law, like charges repel each other. Therefore, the electric force between these two charges will be directed away from each charge.
2. The charge of +2 µC will repel the charge of +3 µC to the right, resulting in a force vector pointing away from the +2 µC charge.
3. Similarly, the charge of +3 µC will repel the charge of +2 µC to the left, resulting in a force vector pointing away from the +3 µC charge.
Now, let’s analyze each option:
- **Diagram W**: Charge +2 µC has a vector pointing left (towards -∞), which is incorrect. Both vectors should point away from each other.
- **Diagram X**: Charge +2 µC has a vector pointing right (correct) and charge +3 µC has a longer vector pointing right. This suggests that the charge +3 µC is experiencing a stronger repulsive force, which is not how it should be represented; both repulsive forces should be equal in magnitude according to Coulomb's law, although the distances might be different.
- **Diagram Y**: Charge +2 µC has a vector pointing right (correct), but charge +3 µC has a vector pointing left (incorrect), since both should repel away from each other.
- **Diagram Z**: Charge +2 µC has a vector pointing right (correct) and charge +3 µC has a smaller vector pointing left. This, too, is incorrect as both should be pointing right.
So, none of the diagrams perfectly represent the situation correctly. However, the most consistent option that follows the rule of repulsion between like charges is Diagram X, but it still inaccurately suggests varying forces or magnitudes.
If you were to select the "least incorrect" representation based on the understanding of the forces involved, **Diagram X** would be the most appropriate choice, but it's important to note that it is not entirely correct. For strict accuracy, all the diagrams need to be revised to show two arrows pointing directly away from each charge.