91Ó°ÊÓ

In the realm of electrostatics, electric potential is a fundamental concept. It represents the potential energy per unit charge at a specified point in an electric field. This means how much work is required to move a unit charge from infinity to that point, without accelerating the charge.
For a point charge, the electric potential, denoted as \( V \), can be determined using the formula:

• \( V = \frac{kQ}{r} \)

where:

• \( k \) is the Coulomb's constant \( (8.99 \times 10^9 \, \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2) \)
• \( Q \) is the magnitude of the charge
• \( r \) is the distance from the point charge

By setting the potential to zero at infinity, we define a reference point that simplifies calculations and comparisons. Here, the electric potential is directly proportional to the charge magnitude and inversely proportional to the distance from the charge. Thus, if you're closer to the charge, the potential increases.

Coulomb's Law offers a detailed explanation of how forces between charged particles operate. It specifically shows how two point charges exert forces on each other, depending on their magnitudes and the distance separating them.
Coulomb's Law is mathematically expressed as:

• \( F = \frac{k |Q_1 Q_2|}{r^2} \)

where:

• \( F \) is the electrostatic force
• \( Q_1 \) and \( Q_2 \) are the magnitudes of the two charges
• \( r \) is the distance between the centers of the two charges

This law helps us understand that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Importantly, this tells us that as charges come closer, the force increases significantly due to the square of the distance term. In the context of our problem, Coulomb's Law underlies the calculations related to the electric field and potential.

Analyzing the direction of an electric field provides insights into how charges will behave within that field. The electric field direction is defined as the direction a positive test charge would move if placed within the field.
In simple terms:

• From a positive charge, the electric field lines radiate outward.
• Toward a negative charge, the electric field lines converge.

This directional behavior helps us predict charge interactions. For instance, when we're told the potential is positive, and if we assume the charge is positive, the field must be moving away from the charge. This fundamental understanding of direction is key in solving various electrostatic problems, such as finding how an unknown charge relates to its surrounding space, as in the initial problem statement. Understanding this, we can infer the electric field direction based on the known charge polarity and the nature of electric field lines.