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Electromagnetism Formula

What is Lorentz Force?

The total electromagnetic force on a moving charge combines the electric force and the magnetic force.

Formula: \vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

Plain-English Meaning

The total electromagnetic force on a moving charge combines the electric force and the magnetic force.

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

Deeper Explanation

The total electromagnetic force on a moving charge combines the electric force and the magnetic force.

Worked Example

Problem: A charge q = 2 μC moves at v = 10⁵ î m/s in E = 100 ĵ V/m and B = 0.01 k̂ T. Find F⃗.

  • F_E = qE⃗ = 2×10⁻⁶ × 100 ĵ = 2×10⁻⁴ ĵ N
  • v⃗ × B⃗ = (10⁵ î) × (0.01 k̂) = 10³ (î × k̂) = −10³ ĵ m/s (since î × k̂ = −ĵ)
  • F_B = qv⃗ × B⃗ = 2×10⁻⁶ × (−10³) ĵ = −2×10⁻³ ĵ N
  • F⃗ = (2×10⁻⁴ − 2×10⁻³) ĵ = −1.8×10⁻³ ĵ N

Result: F⃗ ≈ −1.8×10⁻³ ĵ N

At A Glance

Category: Electromagnetism

Levels covered:

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.