Final answer:
a) Equilateral triangle: net force is zero, b) Along the x-axis: net force is zero on the middle charge, c) Random positions: net force depends on positions, d) All on a single point: net force is zero
Step-by-step explanation:
a) When three point charges are arranged at the vertices of an equilateral triangle, the net force on any one of the charges due to the other two charges is zero. This is because the forces between the charges balance out due to the symmetry of the triangle.
b) When three point charges are arranged along the x-axis at equal intervals, the net force on the middle charge due to the other two charges is zero. This is because the forces between the charges balance out due to the equal distances between them.
c) When three point charges are placed at random positions in space, the net force on any one of the charges due to the other two charges will depend on their positions and magnitudes. It is not guaranteed that the net force will be zero.
d) When all three point charges are located at a single point, the net force on any one of the charges due to the other two charges will also be zero. This is because the distances between the charges is zero, resulting in zero force.