🧲 Magnetic Force Calculator
Lorentz force on a charge (F = qvB) or force on a current-carrying wire (F = BIL).
Result
How to Use This Calculator
Choose between the "Moving Charge" tab (for a charged particle in a magnetic field) and the "Current Wire" tab (for a current-carrying conductor). Select the variable to solve for, fill in the rest, and calculate. The angle θ is between the velocity (or current direction) and the magnetic field vector.
Pick the correct tab: Moving Charge uses F = qvB sin(θ); Current Wire uses F = BIL sin(θ).
For a moving charge, enter charge q in coulombs (a proton is 1.602 × 10⁻¹⁹ C), speed v in m/s, and field B in tesla.
For a wire, enter field strength B in tesla, current I in amperes, and wire length L in metres.
Set the angle θ. Maximum force occurs at θ = 90° (velocity or current perpendicular to field). Zero force at θ = 0° (parallel to field).
Magnetic Force Formula
The magnetic force is always perpendicular to velocity, so it cannot change the speed of a particle, only its direction. This causes charged particles in uniform magnetic fields to travel in circles. The radius of the circular path is r = mv / (qB): larger mass or faster speed gives a wider circle; stronger field or larger charge gives a tighter one.
Worked Examples
Where This Comes Up in Real Life
Electric motors work because a current-carrying coil inside a magnetic field experiences a force. In a DC motor, the coil has n turns of length L each carrying current I in a field B. The total force on one side is F = nBIL (at θ = 90°), and the torque this creates rotates the shaft. A typical small DC motor might have B = 0.3 T, I = 2 A, L = 0.04 m, and n = 50 turns: F = 50 × 0.3 × 2 × 0.04 = 1.2 N per side.
Mass spectrometers use the magnetic force to separate ions by mass. Ions of charge q are accelerated through voltage V, gaining speed v = √(2qV/m). They then enter a magnetic field B and travel in a circle of radius r = mv/(qB). Different masses produce different radii, creating separate spots on a detector. From the spot position, scientists can calculate the mass of the ion and identify the substance. This technique identifies unknown compounds in chemistry labs and detects doping in athletes.
Frequently Asked Questions
What is the magnetic force on a moving charge?
F = qvB sin(θ), where q is charge (C), v is speed (m/s), B is magnetic field strength (T), and θ is angle between velocity and field.
What is the force on a current-carrying wire?
F = BIL sin(θ), where B is field strength (T), I is current (A), L is wire length (m), and θ is angle between current direction and field.
What is the right-hand rule for magnetic force?
Point fingers in the direction of velocity (or current), curl toward B — your thumb points in the direction of the force on a positive charge.
When is the magnetic force zero?
When the charge moves parallel or antiparallel to the field (θ = 0° or 180°), sin(θ) = 0 and there is no force.
Does magnetic force do work?
No! Magnetic force is always perpendicular to velocity, so it cannot do work and cannot change the kinetic energy of a charge.