Explanation:

Introduction:
In electrostatics, Coulomb's Law is the fundamental principle that describes the interaction between charged particles. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Given:
In the given problem, three charges q, q, and -q are placed at the vertices of an equilateral triangle of side l.

Method:
To calculate the force on each charge, we can use Coulomb's Law. The force on a charge q due to another charge Q can be given by:

F = k(qQ/r^2)

where k is Coulomb's constant, r is the distance between the charges, and F is the force on q due to Q.

Calculations:
Let us consider the force on the charge q at one of the vertices due to the other two charges:

The distance between the charges is l, as they are placed at the vertices of an equilateral triangle of side l.

Hence, the force on q due to the charge q at another vertex is:

F1 = k(q^2/l^2)

The direction of this force is towards the other vertex.

Now, the force on q due to the charge -q can be calculated in a similar way. The distance between these charges is also l, and the direction of the force is towards the third vertex.

F2 = k(q*(-q)/l^2)

= -k(q^2/l^2)

Hence, the net force on q is:

Fnet = F1 + F2

= k(q^2/l^2) - k(q^2/l^2)

= 0

Similarly, we can calculate the forces on the other two charges. As the triangle is equilateral, the distances and forces will be the same for all charges.

Hence, the force on each charge is zero.

Conclusion:
In conclusion, the force on each charge q, q, and -q placed at the vertices of an equilateral triangle of side l is zero. This is because the forces due to the other charges cancel out each other.