𧲠Magnetic Force Calculator
Calculate F = qvB for a charged particle in a magnetic field.
Result
How to Use This Calculator
This calculator finds the magnetic force on a moving charge. Enter the charge, its velocity, the magnetic field strength, and the angle between the velocity and the field.
Enter the charge q in coulombs. Use 1.602 x 10^-19 C for a proton, or -1.602 x 10^-19 C for an electron.
Enter the velocity v in meters per second.
Enter the magnetic field strength B in tesla.
Enter the angle in degrees between the velocity direction and the field direction. Use 90 for perpendicular motion, which gives the maximum force.
Click Calculate. The force appears in newtons.
The Magnetic Force Formula
A magnetic field pushes only on moving charges, and only on the part of their motion that cuts across the field lines. That is what the sin(theta) factor says: full force at 90 degrees, zero force at 0 degrees. The force is always perpendicular to both the velocity and the field, which is why the mathematics uses a cross product and physicists reach for the right-hand rule.
Because the force stays perpendicular to the motion, it never does work. A proton spiraling in a magnetic field keeps exactly the same speed lap after lap: the field steers it without speeding it up or slowing it down. This is the opposite of an electric field, which pushes along its own direction and changes kinetic energy.
Worked Example
Where This Comes Up
This formula runs the machinery of modern physics. Particle accelerators steer proton beams with magnetic fields, mass spectrometers sort ions by bending them in arcs, and the aurora happens because Earth's field funnels solar charged particles into spirals near the poles. Old CRT televisions aimed their electron beam with magnetic deflection coils.
The classic mistake is forgetting the angle: students plug in qvB for motion parallel to the field and get a force that should be zero. The other is the sign of the charge. The right-hand rule gives the force on positive charges. Electrons feel the opposite push, so flip the direction for negative q.
Frequently Asked Questions
Which direction does the force point?
Perpendicular to both the velocity and the magnetic field. Point your fingers along v, curl toward B, and your thumb gives the force direction for a positive charge. For electrons, the force points the opposite way.
Why is there no force when the charge moves parallel to the field?
The formula contains sin(theta), and sin(0 degrees) = 0. Physically, the magnetic force comes from the charge cutting across field lines. Moving along them cuts nothing, so nothing pushes.
Does the magnetic force change the particle's speed?
No. The force is always perpendicular to the velocity, so it does zero work. Speed and kinetic energy stay constant while the direction of motion curves, which is why particles spiral instead of speeding up.
What is the Lorentz force?
The full electromagnetic force on a charge: F = q(E + v cross B). This calculator handles the magnetic part, qvB sin(theta). Add qE if an electric field is also present.
What are typical magnetic field values?
Earth's magnetic field is about 30 to 60 microtesla. An MRI magnet is 1.5 to 3 tesla. Particle accelerators steer beams with fields of several tesla.