Introduction:
In this scenario, we have two charges placed at a separation of 10 cm. One charge is positive with a magnitude of 2x10^-6 C, and the other charge is negative with a magnitude of -1x10^-6 C. We need to find the position where a third charge will not experience a net force.

Understanding the forces between charges:
Before we proceed, let's understand the forces between charges. Charges exert electrostatic forces on each other, which can be attractive or repulsive depending on their signs. The magnitude of the 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 (9x10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the two charges, and r is the distance between them.

Calculating the forces:
To find the position where a third charge will not experience a net force, we need to consider the forces exerted by the two existing charges on the third charge. Let's assume the third charge has a magnitude of q3 and is placed at a distance d from the positive charge.

The force exerted by the positive charge on the third charge is given by:

F1 = k * (|q1| * |q3|) / (d^2)

The force exerted by the negative charge on the third charge is given by:

F2 = k * (|q2| * |q3|) / ((10 - d)^2)

Finding the position of net force:
For the third charge to experience no net force, the magnitudes of F1 and F2 should be equal, but their directions should be opposite. Mathematically, this can be expressed as:

F1 = -F2

k * (|q1| * |q3|) / (d^2) = -k * (|q2| * |q3|) / ((10 - d)^2)

Simplifying the equation, we get:

(|q1| * |q3|) / (d^2) = (|q2| * |q3|) / ((10 - d)^2)

Cross multiplying and simplifying further, we obtain:

|q1| * (10 - d)^2 = |q2| * d^2

Substituting the values of q1, q2, and solving the equation will give us the position (d) where a third charge will not experience a net force.

Conclusion:
By calculating the forces exerted by the existing charges on the third charge and equating them, we can find the position where a third charge will not experience a net force. The equation |q1| * (10 - d)^2 = |q2| * d^2 can be solved to determine the exact position.