Compute the magnetic force experienced by a straight wire in a uniform magnetic field. F = I·L·B·sinθ. Visualize current direction, magnetic field vector, and force orientation (right-hand rule).
When a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force. This is the fundamental principle behind electric motors, galvanometers, and railguns. The force is given by F = I (L × B) where I is the current (A), L the length vector (m) in direction of current, and B the magnetic flux density (Tesla). For a straight wire in uniform field, magnitude reduces to F = I·L·B·sinθ, θ being the angle between current direction and magnetic field vector.
The direction follows the right‑hand rule: point fingers along current, curl them toward B‑field, thumb points in direction of force (conventional current). This tool not only calculates numerical magnitude but also determines whether force is "out of the page" (positive I·sinθ) or "into the page" (negative I·sinθ) relative to the standard coordinate system.
In a DC motor, current-carrying loops inside radial magnetic field experience torque. Our calculator helps estimate force per conductor: typical values I=5A, L=0.1m, B=0.4T → F = 0.2 N per wire, crucial for torque predictions.
Railguns use Lorentz force to accelerate projectiles: extremely high currents (megamps) and strong B-fields generate massive forces. For educational models I=500kA, L=10m, B=5T → force ~ 2.5×10⁷ N. Our calculator demonstrates scaling.
You can experimentally verify F = I·L·B·sinθ using a simple setup: suspend a short straight wire between the poles of a permanent magnet (B known from supplier or Hall probe). Pass a DC current (I) through the wire, and measure the deflection or weight change using a precision scale or force sensor. For a horizontal wire with B perpendicular (θ=90°), force F = I·L·B. Compare the measured force with the calculator’s output — typical accuracy within ±5% when accounting for fringe fields and wire alignment. This classic demonstration is described in many undergraduate physics lab manuals (e.g., University Physics Lab, Exp. 8: Magnetic Force on a Wire).
Tip: Use a short, light wire segment (L=0.05 m) and a strong neodymium magnet (B≈0.3 T) with I=2 A → expected force ≈0.03 N, measurable with a milligram scale.
Based on Maxwell's equations and the Lorentz force law formulated by Hendrik Lorentz (1895). The force on a current element is the sum of forces on moving charges. Standard textbooks: “Introduction to Electrodynamics” by David J. Griffiths, “Physics for Scientists and Engineers” by Serway & Jewett. The European Magnetic Field Laboratory (EMFL) and IEEE standards commonly reference these formulas for engineering simulation.
| Parameter | Symbol | Unit | Typical Range |
|---|---|---|---|
| Current | I | Ampere (A) | 0.01 A (sensors) – 10⁵ A (industrial) |
| Length (active segment) | L | meter (m) | mm to meters |
| Magnetic field | B | Tesla (T) | Earth ~5×10⁻⁵ T, MRI ~1-3 T, superconducting ~20 T |
| Force | F | Newton (N) | µN to MN |
In a linear actuator design, engineers need to predict Lorentz force for precise motion. Consider a moving coil with L = 0.15 m, B = 0.65 T, I = 6 A, θ = 90° → F = 0.585 N. If the actuator must lift 0.3 kg weight, required force = mg ≈ 2.94 N, so multiple coils or stronger B needed. This tool allows iterative optimization. The interactive right-hand diagram ensures correct orientation of magnets and current leads.
The vector formula F = I (L × B) uses cross product. Therefore direction is perpendicular to both L and B. sinθ emerges from |L × B| = L·B·sinθ. For θ between 0° and 180°, force direction is given by the sign of I·sinθ (positive if I·sinθ > 0). At θ=90°, maximum force magnitude. In our visualization, current flows to the right (+x direction) for positive I; for negative I the effective physical current reverses (not shown in static arrow, but direction sign flips accordingly). According to right-hand rule: if B points above the wire (θ between 0 and 180, exclusive) and I positive, force points outward. If I negative, force points inward. Our visual uses ⊙ and ⊗ symbols according to I·sinθ sign.
The calculator assumes a straight, rigid wire in uniform magnetic field. For non-uniform fields or curved wires, integration is required. For AC currents, force oscillates with frequency. This tool provides instantaneous force magnitude for DC or RMS for AC if you supply RMS current. Always verify with professional FEA software for high‑precision design.