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
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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.