Lorentz Force Calculator
Find the magnetic force on a moving charge.
The Lorentz force deflects charges moving through a magnetic field.
How the Math Works
The Lorentz Force Calculator uses the formula F = q·v·B·sinθ to determine the magnetic force acting on a moving charge. Here, F represents the force in Newtons, q is the electric charge in Coulombs, v is the velocity of the charge in meters per second, B is the magnetic field strength in Tesla, and θ is the angle between the charge's velocity vector and the magnetic field direction. The sine function (sinθ) accounts for the angle's effect: when the charge moves perpendicular to the field (θ = 90°), sinθ equals 1, maximizing the force. If the motion is parallel to the field (θ = 0°), sinθ is 0, resulting in no force. This vector-based formula captures how magnetic fields interact with moving charges in three-dimensional space.
Practical Applications
This calculation is essential in designing electric motors, where the Lorentz force drives the rotation of coils in a magnetic field, converting electrical energy into mechanical motion. It is also critical in particle accelerators, such as those used in medical radiotherapy or scientific research, where precise magnetic steering ensures charged particles follow controlled paths. Engineers apply this formula to optimize devices like MRI machines, cathode ray tubes, and magnetic levitation systems by predicting how charges behave in magnetic environments, ensuring safety and efficiency in electromagnetic technology.
Day-to-Day Use
While invisible to the naked eye, the Lorentz force underpins many technologies we use daily. For example, the speakers in your headphones rely on electromagnetic coils moving in response to audio signals, a direct application of the Lorentz force. Electric vehicles depend on motor designs governed by these principles to convert electricity into motion. Additionally, MRI machines in hospitals use powerful magnetic fields and radio waves—both influenced by Lorentz force dynamics—to create detailed images of the human body, revolutionizing medical diagnostics. Even the solar panels on satellites must account for charged particles in Earth's magnetosphere, where Lorentz force calculations help protect sensitive electronics from space weather.
Worked example
1 µC at 1000 m/s across 0.5 T → 5 × 10⁻⁴ N.
FAQ
What if motion is along the field?
sin 0° = 0, so there is no magnetic force.