Magnetic Force Calculator
Calculate the magnetic force on a moving charge (Lorentz force) F = qvB sin(θ).
F = |q| × v × B × sin(θ)
What Is the Magnetic Force Calculator?
The Magnetic Force Calculator computes the force on a moving charged particle or current-carrying conductor in a magnetic field. Enter the charge (or current), velocity (or length), magnetic field strength, and the angle between velocity and field to calculate the magnetic force.
Formula
How to Use
For a moving charge: enter charge q (C), velocity v (m/s), magnetic field B (T), and angle θ between v and B. For a current-carrying wire: enter current I (A), wire length L (m), field B (T), and angle θ. The calculator returns force magnitude and, for charges, the radius of circular motion.
Example Calculation
Electron (q=1.6×10⁻¹⁹ C) moving at 10⁶ m/s perpendicular to B=0.01 T: F = 1.6×10⁻¹⁹ × 10⁶ × 0.01 × sin(90°) = 1.6×10⁻¹⁵ N. Wire (I=5A, L=0.2m) in B=0.3T at 90°: F = 0.3×5×0.2×1 = 0.3 N.
Understanding Magnetic Force
The magnetic force on a moving charged particle is one of the four fundamental electromagnetic interactions described by Maxwell's equations. Unlike gravitational and electric forces, the magnetic force acts perpendicular to motion and therefore changes the direction of a particle's path without altering its speed — a property exploited in particle accelerators, mass spectrometers, and plasma confinement devices.
For current-carrying conductors in a magnetic field, the force is the collective magnetic force on all moving charge carriers. This is the principle behind electric motors: current in a conductor experiences a force in a magnetic field, causing rotation. The direction of force is given by the right-hand rule (or Fleming's left-hand rule for motors).
Magnetic force calculations are essential in electromagnetic device design, including DC and AC motors, generators, loudspeakers, magnetic levitation trains, and particle beam steering. Understanding how field strength, current, conductor length, and angle interact determines the torque and efficiency of electrical machines.
Frequently Asked Questions
Why is magnetic force always perpendicular to velocity?
The magnetic force F = qv×B (cross product) is always perpendicular to both v and B. This means it changes the direction of motion but never does work on the charge — it cannot increase kinetic energy.
What is cyclotron motion?
When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force provides centripetal acceleration, causing circular motion. Radius r = mv/(qB). Cyclotrons use this principle to accelerate particles.
What are the units of magnetic field (Tesla)?
1 Tesla = 1 N/(A·m). Earth's field is about 25–65 μT. MRI machines use 1.5–3 T. Powerful research magnets reach 45 T. Neutron stars have fields up to 10¹¹ T.
How does angle affect the force?
The force is maximum when v and B are perpendicular (sin 90°=1), and zero when they are parallel (sin 0°=0). This is because the cross product measures the component of velocity perpendicular to B.
Is this calculator free?
Yes, completely free with no account needed.