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)
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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.