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Understanding the concept of the electric field is essential when studying the forces between charged particles. At a basic level, the electric field is a vector field surrounding an electric charge that exerts force on other charges within the field.

It can be pictorially represented as lines emanating from positive charges and terminating at negative charges. The direction of the electric field at any point is the direction of the force that would be exerted on a positive test charge if it were placed at that point. The concept of the electric field allows us to calculate the force on a charge without having direct contact with the source charge.

For a disk with a uniform positive charge density, the electric field at any point above the center of the disk can be derived from Coulomb's law, scaled with respect to the geometry and charge distribution of the disk. This field is fundamental in determining the force exerted on any charged objects within its influence, like the hovering plastic sphere in the exercise.

Uniform charge density, denoted as \(\sigma\), is a measure of how charge is distributed over a surface. In the context of our exercise, a disk with uniform charge density means that the charge per unit area is constant throughout the entire surface of the disk.

To visualize this, imagine the surface of the disk divided into infinitesimally small areas, each carrying an equal small amount of charge. This uniformity simplifies the calculations of electric fields and forces because it allows for the electric field to be integrated across the entire surface without varying the charge amount per area.

In practical applications, materials with uniform charge distributions are often approximated to make calculations easier. However, in reality, charges might not be perfectly uniform, leading to more complex electric fields and force interactions.

In physics, the calculation of net force is pivotal for understanding how objects will move or interact. The net force is the vector sum of all forces acting on an object. If we have multiple forces, we need to add them vectorially, considering both their magnitudes and directions.

In the context of the exercise, the net force on the plastic sphere is determined by two key forces: the electric force caused by the electric field of the charged disk and the gravitational force pulling the sphere downward. To find where the sphere hovers, we set the net force to zero, which means the electric force exactly cancels out the gravitational force.

More formally, the net force \(F_{net}\) is calculated as the difference between the upward Coulomb force and the downward gravitational force \(F_{g} = Mg\). This net force equation facilitates the determination of the equilibrium position of the sphere—the point at which it hovers motionless above the charged disk. The calculated height at which the net force equals zero provides the height \(h\) where the sphere remains in stable equilibrium.