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Electromagnetism Formula

What is Coulomb's Law?

The electric force between two point charges — the electromagnetic analogue of Newton's gravitation.

Formula: F = k\frac{q_1 q_2}{r^2}

Plain-English Meaning

Charges with the same sign repel each other; opposite charges attract. The force gets weaker with the square of the distance — just like gravity. k ≈ 8.99 × 10⁹ N·m²/C² is a large constant because electric forces are much stronger than gravity.

Keep charge, field, potential, and current distinct. That single habit fixes a large fraction of electromagnetism errors.

Deeper Explanation

F = kq₁q₂/r² where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C². The electric field E = kq/r² and potential V = kq/r created by a point charge. Like Newton's law, it's an inverse-square law — superposition applies for multiple charges.

Worked Example

Problem: Two charges q₁ = +3 μC and q₂ = −2 μC are separated by 0.05 m. Find the force.

  • k = 8.99 × 10⁹ N·m²/C²
  • F = k|q₁q₂|/r²
  • F = 8.99×10⁹ × 3×10⁻⁶ × 2×10⁻⁶ / (0.05)²
  • Numerator = 8.99×10⁹ × 6×10⁻¹² = 0.05394

Result: F ≈ 21.6 N (attractive, as charges have opposite signs)

At A Glance

Category: Electromagnetism

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.