Where:
Magnetic Force (F) = 0 N
The force is perpendicular to both the velocity and the magnetic field.
Where:
Magnetic Force (F) = 0 N
Direction can be determined using the right-hand rule.
Where:
Force per Unit Length (F/L) = 0 N/m
Magnetic force is a fundamental interaction in electromagnetism that affects moving charged particles and current-carrying conductors. It plays a crucial role in technologies from electric motors to particle accelerators and is governed by the Lorentz force law, one of Maxwell's equations. To explore the foundational law that combines electric and magnetic forces, you might find our Lorentz factor calculator useful for understanding high-speed particle behavior.
| Symbol | Quantity | SI Unit | Physical Meaning |
|---|---|---|---|
| F | Magnetic Force | Newton (N) | Force exerted on charged particle or current-carrying conductor |
| q | Electric Charge | Coulomb (C) | Fundamental property of matter; proton: +1.6×10⁻¹⁹ C |
| v | Velocity | Meter/second (m/s) | Speed and direction of charged particle motion |
| B | Magnetic Field | Tesla (T) | Strength of magnetic field; Earth: ~25-65 μT |
| θ | Angle | Degree or Radian | Angle between velocity/wire and magnetic field direction |
| I | Electric Current | Ampere (A) | Flow rate of electric charge; represents moving charges in wire. The relationship between current and other circuit properties is central to Ohm's Law calculations. |
| L | Length | Meter (m) | Length of conductor within magnetic field region |
Step 1: F = qvB sin(θ) → Identify all input variables
Step 2: Convert angle from degrees to radians: θ_rad = θ_deg × π/180
Step 3: Calculate sin(θ_rad) using trigonometric function
Step 4: Multiply q × v × B × sin(θ_rad)
Step 5: Result is magnetic force in newtons (N)
This calculator uses the International System of Units (SI):
Angles are accepted in degrees (0-180°) and internally converted to radians for trigonometric calculations.
Important Clarifications:
Numerical Accuracy: Calculations use JavaScript's double-precision floating point (IEEE 754). Results display in:
This calculator assumes:
Not suitable for: Time-varying fields, relativistic particles, curved conductors, quantum systems, or combined electric+magnetic fields.
A: The sin(θ) term represents the perpendicular component of velocity relative to the magnetic field. At 90°, velocity is completely perpendicular to B, giving maximum force. At 0° or 180°, velocity is parallel to B, resulting in zero force.
A: Use the right-hand rule: Point fingers in direction of velocity (or current), curl them toward magnetic field direction, thumb points in force direction (for positive charges). For negative charges, force is opposite.
A: F = ILB sin(θ) derives from F = qvB sin(θ) by considering many charges moving through wire: I = nqAv_drift, and total force sums over all charges.
A: Magnetic force is always perpendicular to velocity, so it changes direction but not magnitude of velocity. It provides centripetal acceleration for circular motion, a concept also explored in our centripetal force calculator.
This calculator relates to: Lorentz Force Law (full electromagnetic force), Biot-Savart Law (magnetic field from currents), Ampere's Law, Maxwell's Equations, Cyclotron Motion, Hall Effect, and Magnetic Torque on current loops.
This tool is designed for educational purposes, homework verification, and conceptual understanding. For formal academic work, always show your derivation steps and verify calculations independently. The formulas implement standard physics as presented in university-level textbooks like Halliday & Resnick, Griffiths, and Young & Freedman.
Content Accuracy Review: Formulas and physics content reviewed for scientific accuracy. Last comprehensive review: November 2024. Based on standard electromagnetic theory and SI unit conventions.