To determine the net force acting on the -3 C charge located at the top vertex of the equilateral triangle, we need to consider the forces exerted by the other two -4 C charges located at the bottom vertices.
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Understanding the Configuration and Forces:
- The charge at the top of the triangle (-3 C) will experience a repulsive force from both -4 C charges at the bottom. Since similar charges repel each other, the forces will act away from the two -4 C charges.
- Let's denote the force exerted by the left -4 C charge (lower left corner) as \( F_{L} \) and the force exerted by the right -4 C charge (lower right corner) as \( F_{R} \).
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Calculating the Direction of Each Force:
- The charge on the left (-4 C) will exert a force directed to the left (towards the left charge) at an angle toward the vertical due to the position of the charges.
- The charge on the right (-4 C) will exert a force directed to the right (towards the right charge) at an angle toward the vertical.
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Force Vectors:
- Let's analyze the forces in terms of their components:
- The force from the left charge has components:
- A horizontal component to the left.
- A vertical component downward.
- The force from the right charge has components:
- A horizontal component to the right.
- A vertical component downward.
- The force from the left charge has components:
- Let's analyze the forces in terms of their components:
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Net Force Calculation:
- The vertical components from both left and right -4 C charges add together, creating a total downward force.
- The horizontal components from both charges will cancel each other out, as one pushes left and the other pushes right.
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Conclusion:
- The net force acting on the top -3 C charge will be directed straight down (towards the -4 C charges below).
- In the context of the vectors labeled in the diagram, this direction corresponds with the vector labeled Y.
Thus, the vector that best represents the net force acting on the -3 C charge in the diagram is Y.
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