Questions on Coulomb’s Law

General Formula for Coulomb’s Law

Coulomb’s Law describes the electric force exerted between two charges, denoted as (q1) and (q2). The relationship is expressed mathematically as follows:

Force = (k × q1 × q2) / r², where:

• k = 8.99 × 10⁹ N·m²/C².
• r = the distance between the charges.

It is important to note that force is a vector quantity. Therefore, when multiple charges act on a single charge, the net force is determined by the vector sum of the individual forces. Additionally, opposite charges attract each other, while like charges repel.

Examples of Coulomb’s Law Applications

Example 1

Question: Two charges, each with values of +3 × 10^-9 C and -5 × 10^-9 C, are separated by a distance of 2 meters. What is the magnitude of the electric force between them, and what type of force is it?

Solution:

• Identify the requirement: We need to calculate the magnitude of the electric force between the two charges, with the given charge values and distance.
• Method for solving the problem: Utilize Coulomb’s Law to compute the electric force; the formula is Force = (k × q1 × q2) / r².
• Data identification: q1 = +3 × 10^-9 C, q2 = -5 × 10^-9 C, r = 2 m. It is known that k = 9 × 10⁹ N·m²/C².
• Unit verification: All units conform to the International System of Units (SI).
• Calculate the force magnitude by applying Coulomb’s Law: Force = (9 × 10⁹) × (3 × 10^-9) × (-5 × 10^-9) / (2² = 3.37 × 10^-8 N. Since the charges are different, the type of electric force is “attractive.”

Example 2

Question: Consider two charges, both +6 nanoCoulombs and +1 nanoCoulomb, separated by a distance of 2 millimeters. What is the magnitude of the electric force between them (electrostatic force)?

Solution: F = k × q1 × q2 / r²
= (9 × 10⁹) × (6 × 10^-9) × (1 × 10^-9) / (2 × 10^-3)²
= 1.35 × 10^-2 N.
The nature of the electric force is “repulsive” because the charges are alike.

Example 3

Question: Two charges of +1 Coulomb and -3 Coulombs are separated by a distance of 3 meters. What is the magnitude of the attractive electric force between them?

• Solution:
• Given data: q1 = +1 Coulomb, q2 = -3 Coulombs, r = 3 meters.
• By substituting values into Coulomb’s Law, the force is calculated as: 9 × 10⁹ × (1) × (3) / (3²).
• So, the electric force equals 3 × 10⁹ N.