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A point charge is a charge that is concentrated at a single point in space. It is an idealized concept, meaning in practical scenarios, actual charges are spread over a finite space, but for simplicity in calculations and understanding electric fields, we often treat them as point charges.

Understanding a point charge helps in calculating the electric field and potential at different locations. The electric field around a point charge decreases with the square of the distance from the charge, while the potential decreases with the distance. Imagine a point charge as a source of influence on the surrounding space; this influence diminishes as one moves further away from the charge.

In our given exercise, the charge influences two specific points (A and B) and creates a potential difference between them due to its existence alone.

Coulomb's Law is fundamental to understanding electrostatic interactions. It describes the force between two point charges. The formula for Coulomb's Law is: \[ F = k_e \frac{|q_1 \, q_2|}{r^2} \]Here:

• \(F\) is the force between the charges.
• \(k_e\) is the Coulomb constant \(8.99 \times 10^9 \, \mathrm{N \cdot m^2/C^2}\).
• \(q_1\) and \(q_2\) are the magnitudes of the charges.
• \(r\) is the distance between the centers of the two charges.

This force can be attractive if the charges are of opposite signs or repulsive if they have the same sign.

In the context of electric potential, Coulomb's Law also assists in determining how point charges interact with each other and the surrounding electric field. In our problem, although it primarily focuses on electric potential, Coulomb’s Law principles ensure comprehending how the field interactions contribute to potential differences.

An electric field represents the influence a charge exerts on the surrounding space, affecting other charges that enter this space. It is a vector field, meaning that it has a direction and magnitude. The strength of the electric field \(E\) created by a point charge \(q\) is given by the formula:

\[ E = \frac{k_e \cdot q}{r^2} \]

where \(r\) is the distance from the point charge.

• Direction: Outward from the charge if positive, inward if negative.
• Units: Newtons per Coulomb (N/C).

In our exercise context, the negative sign of the charge means the electric field direction from this charge is inward, extending towards the charge itself. This behavior inversely influences the potential difference between points A and B, as the field dictates the rate at which the electric potential changes as you move along its direction.

Electric potential difference, also known simply as voltage, is a measure of the difference in electric potential energy per unit charge between two points. It shows how much energy work is done by moving a charge between two points in an electric field.

The relationship between the electric potential difference and a point charge’s potential at a distance \(r\) is described by the formula:\[ V = k_e \cdot \frac{q}{r} \]

• \(V\): Electric potential (volts).
• \(q\): The point charge creating the potential.
• \(r\): The distance from the charge.

In the original exercise, the potential difference \(V_B - V_A = 45 \mathrm{V}\) tells us how energy per unit of charge changes as we move from point A to point B. The negative value of the charge along with this positive difference indicates that point A is at higher potential energy compared to point B, hence showing the direction of electric field and potential energy shift.