A moving charge in a magnetic field feels a push
A charge sitting still ignores a magnetic field. Set it moving and the field pushes on it — sideways to both the motion and the field.
Here q is the charge, v its speed, B the field strength and θ the angle between the velocity and the field. It is the force behind electric motors, particle accelerators and the aurora.
Direction: the right-hand rule
Point your fingers along the velocity, curl them toward the field, and your thumb gives the force on a positive charge. For a negative charge it is the other way around.
Why the angle matters
The sine means a charge moving straight along the field feels nothing at all (θ = 0°), while one moving across it feels the full force (θ = 90°). The calculator shows that swing as you change the angle.
Frequently asked questions
What is the magnetic force formula?
For a moving charge, the Lorentz force is F = q·v·B·sinθ, where q is the charge, v its speed, B the magnetic field strength and θ the angle between the velocity and the field. The force is in newtons.
Why does a stationary charge feel no magnetic force?
Because the force depends on velocity. With v = 0 the formula gives zero. A charge must be moving through the field to feel a magnetic push; a still charge only responds to electric fields.
What is the right-hand rule?
A way to find the force's direction. Point your fingers along the velocity, curl them toward the field, and your thumb points along the force on a positive charge. For a negative charge the force is the opposite way.
Why does the angle matter?
The sinθ term means a charge moving straight along the field (θ = 0°) feels no force at all, while one moving across it (θ = 90°) feels the full force. In between, only the perpendicular part of the motion counts.
What is the force on a current-carrying wire?
A related formula, F = B·I·L·sinθ, gives the force on a wire of length L carrying current I in a field B. It is the same physics as the moving charge and is what makes electric motors turn.