To solve this problem, we can use the principle of electrostatic equilibrium. In order for the system of charges to be in equilibrium, the net force acting on each charge must be zero.

Let's consider the forces acting on the charge q at the centroid. Since the charges at the vertices of the equilateral triangle are all positive (+Q), they will exert repulsive forces on the charge q.

The force between two charges can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

Since the charges at the vertices are equidistant from the centroid, the forces they exert on the charge q will have the same magnitude. Let's call this force F.

Now, let's consider the forces acting on one of the charges at the vertices. The other two charges at the vertices will exert repulsive forces on this charge. Again, these forces will have the same magnitude F.

Since the charges at the vertices are also equidistant from each other, the forces they exert on each other will also have the same magnitude F.

Since the system is in equilibrium, the net force acting on each charge must be zero. Therefore, the sum of the forces acting on the charge q at the centroid must be zero.

Since there are three forces of magnitude F acting on the charge q, they must add up to zero. This means that the magnitude of the force F must be equal to the sum of the magnitudes of the forces exerted by the charges at the vertices on each other.

Therefore, we can write the equation:

3F = 3F

This equation tells us that the magnitude of the force F is equal to itself, which is always true.

Hence, the system of charges is in equilibrium when a charge q is placed at the centroid of an equilateral triangle with three charges of magnitude +Q at the vertices.

Question

To solve this problem, we can use the principle of electrostatic equilibrium. In order for the system of charges to be in equilibrium, the net force acting on each charge must be zero.

Let's consider the forces acting on the charge q at the centroid. Since the charges at the vertices of the equilateral triangle are all positive (+Q), they will exert repulsive forces on the charge q.

The force between two charges can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

Since the charges at the vertices are equidistant from the centroid, the forces they exert on the charge q will have the same magnitude. Let's call this force F.

Now, let's consider the forces acting on one of the charges at the vertices. The other two charges at the vertices will exert repulsive forces on this charge. Again, these forces will have the same magnitude F.

Since the charges at the vertices are also equidistant from each other, the forces they exert on each other will also have the same magnitude F.

Since the system is in equilibrium, the net force acting on each charge must be zero. Therefore, the sum of the forces acting on the charge q at the centroid must be zero.

Since there are three forces of magnitude F acting on the charge q, they must add up to zero. This means that the magnitude of the force F must be equal to the sum of the magnitudes of the forces exerted by the charges at the vertices on each other.

Therefore, we can write the equation:

3F = 3F

This equation tells us that the magnitude of the force F is equal to itself, which is always true.

Hence, the system of charges is in equilibrium when a charge q is placed at the centroid of an equilateral triangle with three charges of magnitude +Q at the vertices.

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