Coulomb’s Law

1. Definition

Coulomb’s Law states that the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Coulomb's Law Diagram

1.1. In Formula Form

F = k · (q₁ · q₂) / r²

Where:

  • F : Electric force between the charges
  • k : Coulomb’s constant (≈ 8.99 × 10⁹ N·m²/C²)
  • q₁, q₂ : Magnitudes of the charges (in Coulombs)
  • r : Distance between the charges (in meters)

1.2. Other Variations

  • Vector Form: F = k · (q₁ · q₂ / r²) · r̂ where r̂ is the unit vector pointing from one charge to the other.

  • If the charges have the same sign → the force is repulsive.

  • If the charges have opposite signs → the force is attractive.

1.3. Unit of Measurements

  • Force (F): Newton (N)
  • Charge (q): Coulomb (C)
  • Distance (r): meter (m)
  • Coulomb’s constant (k): N·m²/C²

1.4. Example

If q₁ = 2 C, q₂ = 3 C, and r = 2 m: F = (8.99 × 10⁹) × (2 × 3) / (2²) => F = (8.99 × 10⁹ × 6) / 4 => F = (53.94 × 10⁹) / 4 => F = 13.485 × 10⁹ N

2. Usage

2.1. Calculations

Coulomb’s Law helps you calculate:

  1. The magnitude of electric force between two charges
  2. Whether the force is attractive or repulsive
  3. The effect of changing distance or charge magnitude on the force

2. Applications

It is used in:

  1. Analyzing electrostatic forces in physics problems
  2. Designing capacitors and other charge-storage devices
  3. Understanding molecular bonding and interactions in chemistry
  4. Studying atomic structure and electron behavior

3. Limitations

It is important to note that Coulomb’s Law has the following limitations:

  • It applies only to point charges or spherical charge distributions.
  • It assumes the charges are stationary (not moving).
  • It is accurate only when the medium is uniform (like a vacuum or air, unless adjusted for permittivity).
  • It ignores quantum effects at very small scales.

4. Video Explanation

video coming soon