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Electric potential energy is a form of energy associated with the positions of charged particles relative to each other. When two charges are involved, as with the small metal spheres in our example, the electric potential energy reflects their potential to interact via electrical forces.

This energy arises from the electrostatic forces between the charges. The formula for calculating the electric potential energy between two point charges is \[ U = k \frac{q_1 q_2}{r} \]where:

• \( U \) is the electric potential energy,
• \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \text{ Nm}^2/\text{C}^2 \),
• \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
• \( r \) is the distance between the charges.

In our scenario, we see how this energy changes as the distance between the charged spheres shifts from 0.800 m to 0.400 m. The change in electric potential energy is crucial in determining new velocities of the spheres as they draw closer.

Kinetic energy is the energy of motion. It is defined by how fast an object is moving and its mass. In the context of moving charges, kinetic energy can be transformed into other energy forms, such as electric potential energy, as they interact with each other.

The basic formula for calculating kinetic energy is:\[ KE = \frac{1}{2} mv^2 \]where:

• \( KE \) is the kinetic energy,
• \( m \) is the mass of the object,
• \( v \) is the velocity of the object.

In the exercise, when the metal sphere with charge \( q_2 \) moves towards \( q_1 \) with an initial speed, it possesses kinetic energy. As it approaches the other charge, some of this kinetic energy is transformed into potential energy, reducing its speed until it reaches its closest point of approach.

Point charges are theoretical charges that act as if they are concentrated at a single point in space. This simplification allows us to ignore the actual size of the objects and focus solely on the effects of charge and distance.

In physics problems like the one at hand, treating objects as point charges lets us focus on the fundamental principles of charge interaction without worrying about more complex spatial properties.

This approximation works well for many problems, offering a good understanding of electrostatic interactions between charged bodies by simplifying calculations. Thus, in our exercise, it is assumed that both spheres are point charges, making the calculations manageable while accurately illustrating the core principles of electrostatics.

Electrostatics is a branch of physics dealing with stationary or slow-moving electric charges. This field focuses on the forces and fields created by these charges, which are foundational to understanding many principles of electricity and magnetism.

Culminating in Coulomb's Law, electrostatics describes how charged objects exert forces on each other based on their charges and separation distance. In our example:

• The two charged spheres repel each other because like charges repel.
• Electrostatic forces result in changes in kinetic and potential energy as the distance between charges varies.

Understanding electrostatics involves comprehending conservation of energy principles, especially when dealing with mechanical energies such as kinetic and electric potential energy. This understanding allows us to predict motion and energy changes as charges interact.