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Understanding Coulomb's Law is essential when studying electrostatic forces between two point charges. It states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

Mathematically, this is expressed as: \[F = k \frac{|q_{1}q_{2}|}{r^2}\], where:

• \(F\) is the magnitude of the electric force between the charges,
• \(k\) is Coulomb's constant (approximately \(9.0 \times 10^9 \text{ Nm}^2/\text{C}^2\)) and represents the electrostatic force constant,
• \(q_1\) and \(q_2\) are the quantities of the two charges,
• \(r\) is the distance between the centers of the two charges.

Note that Coulomb's Law applies to point charges or charge distributions that are spherically symmetric, assuming that their sizes are much smaller than the distance between them. The electric force calculated using this law is a vector quantity and can be attractive or repulsive depending on the nature of the charges involved.

The electric charge is a fundamental property of particles that determines how they interact with electromagnetic fields. There are two types of charges commonly discussed: positive and negative. Like charges repel each other, while unlike charges attract each other.

In the case mentioned in the exercise, both point charges have positive values, which, according to the principle of charge interaction, will result in a repulsive force between the charges. The unit of electric charge is the coulomb (\(C\)). Lowercase \(q\) often denotes the symbol for charge in equations. Microcoulombs (\(\mu C\)) are a smaller unit of charge where 1 microcoulomb equals \(1 \times 10^{-6}\) coulombs. Managing the conversion between these units correctly is essential in performing accurate electric force calculations. Additionally, electric charge can be understood in the context of quantization, where all charge in the universe is a whole-number multiple of the elementary charge carried by a single proton or electron.

The concept of acceleration due to electric force comes into play when a charged particle experiences a change in its velocity due to the electrostatic force exerted on it by other charges. This acceleration is calculated using Newton’s second law of motion, which states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass (\(A = F/m\)).

In our exercise, the small sphere with charge \(q_{2}\) is experiencing a repulsive force from charge \(q_{1}\), due to both being positive charges. By calculating the electric force using Coulomb’s Law and then dividing it by the mass of the sphere, we obtain the acceleration. It is important to note that the electric force can change as the distance between charges changes, but in this problem, we are asked to find the instantaneous acceleration when the speed of the sphere is a specific value at a certain distance, ignoring any potential change in that distance over time. Since the given exercise neglects gravity, the only force to consider in the calculation of acceleration is the electrostatic force, thus simplifying the problem at hand.