Magnetic Force Calculator (F = BIL and F = qvB)

Magnetic Force Guide

Force on a Current-Carrying Wire

F = BIL sin θ. Where B = magnetic flux density (tesla, T), I = current (A), L = length of conductor in the field (m), θ = angle between conductor and field. Maximum force when θ = 90° (conductor perpendicular to field). Zero force when θ = 0° (conductor parallel to field). Example: a 10 cm wire carrying 2A in a 0.5T field at 90°: F = 0.5 × 2 × 0.1 × sin(90°) = 0.1N. Direction: Fleming's left-hand rule — first finger: field direction (north to south), second finger: conventional current direction

Force on a Moving Charge

F = qvB sin θ. Where q = charge (C), v = velocity (m/s), B = magnetic flux density (T), θ = angle between velocity and field. An electron (q = 1.6×10⁻¹⁹ C) moving at 1×10⁶ m/s perpendicular to a 0.5T field: F = 1.6×10⁻¹⁹ × 10⁶ × 0.5 = 8×10⁻¹⁴ N. This tiny force is huge compared to the electron's weight (9.1×10⁻³⁰ kg × 9.81 = 8.9×10⁻²⁹ N). Magnetic force does no work on a charge — it only changes direction, never speed. This is why charged particles move in circles (not spirals) in uniform magnet

Circular Motion in Magnetic Field

The magnetic force provides the centripetal force: qvB = mv²/r. Therefore radius r = mv/(qB). Larger mass, higher speed, weaker field → larger radius. Larger charge, stronger field → smaller radius. A proton (m=1.67×10⁻²⁷ kg, q=1.6×10⁻¹⁹ C) at 10⁷ m/s in a 1T field: r = (1.67×10⁻²⁷ × 10⁷)/(1.6×10⁻¹⁹ × 1) = 0.104m. The cyclotron (particle accelerator) uses this principle — particles spiral outward as they are accelerated, with the radius increasing as speed increases.

Applications

Electric motors: F=BIL force on current-carrying coils in a magnetic field produces rotation. The motor effect. Loudspeakers: current through a coil in a magnetic field creates oscillating force, vibrating the cone. Cathode ray tubes (oscilloscopes, old TVs): electron beam deflected by magnetic force for scanning. Mass spectrometer: ions of different mass have different radii in the same field — allows separation and identification of isotopes. MRI scanners: strong magnetic fields (1.5-3T) align