To analyze the forces acting on charge \( +q \) from the other two charges, let’s denote the charges and their positions in the equilateral triangle.
Assume the following placements:
- Charge \( +q \) is at the bottom corner (let’s say point A).
- Charge \( +Q \) is at the top corner (point B).
- Charge \( -Q \) is at the left corner (point C).
(a) Direction of the net force on charge \( +q \)
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Force due to charge \( +Q \): Because both \( +q \) and \( +Q \) have the same positive charge, the force exerted by \( +Q \) on \( +q \) will be repulsive. This force will act directly away from \( +Q \) towards point A (the position of \( +q \)), which is directed downward at an angle toward point B.
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Force due to charge \( -Q \): The charge \( -Q \) attracts \( +q \), leading to a force that pulls \( +q \) toward \( -Q \). This force acts along the line connecting the two charges (which points up and to the left).
When you combine these two forces, you find that the force due to \( -Q \) (attractive) has a component that pulls \( +q \) to the left and upward, while the force due to \( +Q \) (repulsive) pulls it downward and slightly to the right.
To determine the net effect, calculate the force vectors' components. The net force's direction is found based on the combination of these forces, which overall tends toward the left and upwards as downward force from \( +Q \) is countered by the upward attraction to \( -Q \).
Conclusion:
The net force on charge \( +q \) is more directed to the left and upward due to the attractive force from \( -Q \) outweighing the repulsive force from \( +Q \).
(b) Total electric force on the system of three charges
The total electric force on the system of three charges needs to be calculated as follows:
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Force between \( +q \) and \( +Q \): This is a repulsive force given by Coulomb's law: \[ F_{qQ} = k \frac{|qQ|}{r^2} \] where \( r \) is the distance between \( +q \) and \( +Q \).
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Force between \( +q \) and \( -Q \): This is an attractive force, also given by Coulomb's law: \[ F_{q(-Q)} = k \frac{|qQ|}{r^2} \]
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Force between \( +Q \) and \( -Q \): There is also a force between \( +Q \) and \( -Q \), which is also attractive: \[ F_{Q(-Q)} = k \frac{|Q^2|}{r^2} \]
However, when we look at the total force acting on the system of charges, we find that the forces that the charges exert on each other are internal forces (for every action, there is an equal and opposite reaction), and they do not contribute to the net external force acting on the entire system as long as we're considering these three charges without any external influence.
Conclusion:
The total electric force of the system of three charges is effectively zero: \[ F_{\text{total}} = 0 \text{ N} \]
This is because the internal electric forces between the charges cancel each other out as per Newton's third law, leading to no net movement of the system as a whole.
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