Net force on charqe Q is zero as all the vector will cut off each other

Force on a Charge at the Centroid of an Equilateral Triangle

The force experienced by a charge at the centroid of an equilateral triangle can be determined by considering the individual forces exerted by each of the charges q1, q2, and q3.

Definition of Centroid
The centroid of a triangle is the point where all three medians intersect. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposing side. In an equilateral triangle, all three medians are concurrent at a single point, which is the centroid.

Calculating the Force
To determine the force on a charge Q placed at the centroid, we need to consider the forces exerted by each of the charges q1, q2, and q3 individually and then find their vector sum.

1. Force due to q1:
The force exerted by q1 on Q can be calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
- The distance between q1 and Q is l/√3, as the centroid divides each median in a 2:1 ratio.
- The force exerted by q1 on Q is given by F1 = k * (Q * q1) / (l/√3)^2, where k is the electrostatic constant.

2. Force due to q2:
Similar to q1, the force exerted by q2 on Q can be calculated using Coulomb's Law.
- The distance between q2 and Q is also l/√3.
- The force exerted by q2 on Q is given by F2 = k * (Q * q2) / (l/√3)^2.

3. Force due to q3:
The force exerted by q3 on Q can be found using Coulomb's Law as well.
- The distance between q3 and Q is also l/√3.
- The force exerted by q3 on Q is given by F3 = k * (Q * q3) / (l/√3)^2.

Vector Sum of Forces
The force on Q at the centroid is the vector sum of the forces exerted by q1, q2, and q3.
- The total force on Q is given by the vector sum: F_total = F1 + F2 + F3.

Explanation
When charges q1, q2, and q3 are placed at the vertices of an equilateral triangle, they create an electric field around them. This electric field exerts forces on any other charges placed within it. The force experienced by a charge at the centroid of the triangle is the result of the combined effect of the electric fields created by q1, q2, and q3.

By calculating the individual forces exerted by each charge using Coulomb's Law and then summing them as vectors, we can determine the total force on the charge Q at the centroid.

It is important to note that the forces on Q due to q1, q2, and q3 will have both magnitude and direction. The direction of each force will depend on the relative positions of the charges and the sign