The problem states that three charges, each of 5 microcoulombs, are placed at the center of an equilateral triangle with a side length of 10 cm. We need to determine the force exerted on a charge of 1 microcoulomb placed at the center of the triangle.

Let's break down the problem into smaller steps to solve it:

1. Calculating the distance between the charges:
- Since we have an equilateral triangle, all the sides are equal. Therefore, the distance between the charges is also 10 cm.

2. Calculating the electric force between two charges:
- The electric force between two charges can be calculated using Coulomb's Law:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

3. Calculating the force on the charge of 1 microcoulomb:
- To find the force on the charge of 1 microcoulomb, we need to calculate the forces exerted by each of the three 5 microcoulomb charges and then add them vectorially.
- Since the charges are at the center of the triangle, the forces will act along the sides of the equilateral triangle and form a closed triangle.

- Let's calculate the force between the charge at the center and one of the 5 microcoulomb charges:
F1 = (9 × 10^9 N m^2/C^2) * ((5 × 10^-6 C) * (1 × 10^-6 C)) / (0.1 m)^2
= 45 N

- The magnitude of the force between the charge at the center and each of the three 5 microcoulomb charges is 45 N.

- Since the forces are acting along the sides of the equilateral triangle and form a closed triangle, the resultant force will be zero. This is because the forces cancel out each other due to the symmetry of the triangle. Therefore, the net force on the charge of 1 microcoulomb placed at the center of the triangle is zero.

In conclusion, the force exerted on the charge of 1 microcoulomb placed at the center of the equilateral triangle, where three charges of 5 microcoulombs each are located, is zero.