Magnetic Force Calculator

The magnetic force is the component of the electromagnetic force that acts on a moving electric charge or current-carrying conductor when it is in a magnetic field. This force is described by the Lorentz force law and is fundamental to electric motors, generators, particle accelerators, and many other technologies.

Force on a Moving Charge

When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field:

F = q × v × B × sin(θ)

Where:

• F = magnetic force (Newtons, N)
• q = electric charge (Coulombs, C)
• v = velocity of the particle (meters per second, m/s)
• B = magnetic field strength (Tesla, T)
• θ = angle between velocity vector and magnetic field vector

The force is maximum (θ = 90°) when velocity is perpendicular to the field, and zero (θ = 0°) when velocity is parallel to the field.

Force on a Current-Carrying Wire

A wire carrying current in a magnetic field experiences a force:

F = I × L × B × sin(θ)

Where:

• I = current (Amperes, A)
• L = length of the wire in the field (meters, m)
• B = magnetic field strength (Tesla, T)
• θ = angle between wire and field

This is the principle behind electric motors: current in the armature windings interacts with the motor’s magnetic field to produce rotational force (torque).

Magnetic Field Strength Reference

Direction of the Force

The direction of the magnetic force is given by the right-hand rule: point fingers in the direction of velocity (or current), curl toward the magnetic field, and the thumb points in the direction of force (for positive charges).

The magnetic force does no work. Because F is always perpendicular to v, the dot product F·v is zero. That means a magnetic field can change the direction of a charged particle’s motion but never its speed or kinetic energy. This is the deep reason why magnetic fields are used for steering charged beams (mass spectrometers, particle accelerators, electron microscopes) but never for accelerating them, which requires an electric field.

Circular motion in a uniform field. A charged particle moving perpendicular to a uniform magnetic field travels in a circle. Setting the magnetic force equal to the centripetal force gives:

r = mv / (qB)

where r is the radius, m is the particle mass, v is the speed, q is the charge magnitude, and B is the field strength. This relationship is what makes mass spectrometers work: ions of different mass-to-charge ratios trace different radii and land at different detector positions. Cyclotrons and synchrotrons exploit the same principle on a much larger scale.