Solution:

Given: Three charges q, q, -q are placed at the corner of the equilateral triangle of side a.

To find: The electric potential at the centroid of the triangle.

Electric Potential:

The electric potential at a point in an electric field is defined as the amount of work done per unit charge in bringing a small test charge from infinity to that point without acceleration.

Formula:

The electric potential (V) at a point due to a point charge q at a distance r from it is given by:

V = kq / r

Where k is the Coulomb's constant.

Electric Potential at Centroid of Equilateral Triangle:

To find the electric potential at the centroid of the equilateral triangle, we need to find the net electric potential due to the three charges at the centroid.

The centroid of an equilateral triangle is the point of intersection of its medians. The medians of an equilateral triangle divide each other in the ratio 2:1.

Let the charges q, q, and -q be placed at the vertices of an equilateral triangle of side a.

Let G be the centroid of the triangle.

The distance of G from each vertex is (2/3)a.

The electric potential due to the charge q at G is:

V1 = kq / (2/3)a = (3/2)kq / a

The electric potential due to the charge -q at G is:

V2 = -kq / (2/3)a = -(3/2)kq / a

The electric potential due to the charge q at G is:

V3 = kq / (2/3)a = (3/2)kq / a

The net electric potential at G is given by:

V = V1 + V2 + V3 = (3/2)kq / a - (3/2)kq / a + (3/2)kq / a = 0

Therefore, the electric potential at the centroid of the equilateral triangle is zero.

Conclusion:

The electric potential at the centroid of the equilateral triangle of side a due to the charges q, q, and -q placed at its vertices is zero.