Explain Coulomb’s Law and its mathematical form.

Coulomb’s Law describes the electrostatic force between two point charges. It states that the force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This force is attractive if the charges are of opposite sign and repulsive if the charges are of the same sign.

Mathematical Form of Coulomb’s Law:

The mathematical expression for Coulomb’s law is:

F=ke.∣q1q2∣/r2

Where:

  • F is the magnitude of the electrostatic force between the two charges.
  • and q2 are the magnitudes of the two point charges.
  • r is the distance between the centers of the two charges.
  • ke is Coulomb’s constant, which is approximately 8.99×109 N⋅m2/C2
  • The absolute value ∣q1q2∣ ensures the force is positive, and the direction is determined by the signs of the charges.

Key points about Coulomb’s Law:

    1. Proportionality: The force increases with the product of the magnitudes of the charges. Larger charges result in a stronger force.
    2. Inverse Square Law: The force decreases with the square of the distance between the charges. Doubling the distance between the charges reduces the force by a factor of four.
    3. Nature of the Force:
      • If both charges have the same sign (both positive or both negative), the force is repulsive.
      • If the charges have opposite signs (one positive, one negative), the force is attractive.

    Coulomb’s Law applies to point charges or spherical charge distributions, and it’s fundamental to understanding electrostatic interactions in physics

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