MotionLab

Magnetic Force Calculator

Moving charges feel a sideways push in a magnetic field — the force that makes electric motors spin.

Charge (C)

Velocity (m/s)

Magnetic field (T)

Angle between v and B (°)

Magnetic force (N)

F = |q|vB sin(θ)

What you entered

Charge (C): 1.602e-19Velocity (m/s): 1000000Magnetic field (T): 0.5Angle between v and B (°): 90

1
sin(θ)
sin(90°)= 1
2
F = |q|vB sin(θ)
|1.60e-19| × 1000000 × 0.5 × 1= 8.0100e-14 N

Result

Magnetic force (N): 0

A charge of 1.60e-19 C moving at 1.00e+6 m/s through a 0.5 T field at 90° experiences a force of 8.0100e-14 N.

Lorentz force on a moving charge for standard particle setups

Each row is F = |q| x v x B x sin(theta) with the four inputs this calculator takes. The first row is a proton crossing a laboratory field at a right angle, which is the calculator's own default.

Charge q (C)	Speed v (m/s)	Field B (T)	Angle (deg)	Force (N)
1.602e-19	1e6	0.5	90	8.0100e-14
1.602e-19	1e6	0.5	45	5.6639e-14
1.602e-19	1e6	0.5	30	4.0050e-14
1.602e-19	1e6	0.5	0	0.0000e+0
1.602e-19	1e6	1.5	90	2.4030e-13
1.602e-19	1e7	0.01	90	1.6020e-14
1.602e-19	1e5	5e-5	90	8.0100e-19
3.204e-19	1e6	0.5	90	1.6020e-13
1e-6	500	0.2	90	1.0000e-4

1.602e-19 C is one elementary charge, so rows 1 to 7 are a single proton and row 8 is an alpha particle carrying twice that charge, which doubles the force. Row 4 shows the charge moving along the field lines, where sin(0) is zero and so is the force. The 1.5 T row is a clinical MRI field and the 5e-5 T row is roughly Earth's magnetic field. Forces are given in scientific notation, as the step-by-step working prints them.

The force is always perpendicular

Unlike gravity or electric forces, the magnetic force is always perpendicular to both the velocity and the magnetic field — this is why it can change a particle's direction but never its speed, causing charged particles to move in circles (or spirals) in uniform magnetic fields.

The sin(θ) factor is crucial

When a charge moves parallel to the field lines (θ = 0° or 180°), the magnetic force is zero — it only feels the full force when moving perpendicular (θ = 90°). This angle dependence is why particle accelerators and mass spectrometers are carefully designed to control the orientation of particles relative to the field.

Frequently asked questions

A proton (q = 1.6×10⁻¹⁹ C) moves at 10⁶ m/s perpendicular to a 0.5 T field. What force acts on it?

F = qvBsin(θ) = 1.6×10⁻¹⁹ × 10⁶ × 0.5 × sin(90°) = 8×10⁻¹⁴ N. This force is always perpendicular to the velocity, so the proton moves in a circle with radius r = mv/(qB) = 0.021 m ≈ 2.1 cm.

Why doesn't magnetic force do work on charged particles?

Because the force is always perpendicular to velocity, it changes the particle's direction but never its speed. Work = F·d·cos(θ), and with θ = 90° between force and velocity, W = 0. A magnetic field can steer particles but cannot speed them up or slow them down.

How do electric motors use magnetic force?

Current-carrying wires in a magnetic field experience F = BIL×sin(θ). The motor's coil has current flowing perpendicular to the permanent magnet's field, producing a torque that spins the rotor. Reversing current direction (via a commutator or electronics) keeps the rotation going continuously.

What's the difference between magnetic force and electric force?

Electric force (F = qE) acts on any charge, moving or stationary, and points along the field. Magnetic force (F = qvBsin(θ)) only acts on moving charges and is always perpendicular to both velocity and field. A stationary charge feels no magnetic force at all. See the Coulomb's law and electric field calculators.

How do mass spectrometers use magnetic force?

Ions with different masses but the same charge and velocity enter a magnetic field. The radius of their circular path is r = mv/(qB) — heavier ions curve less. By measuring the radius, the spectrometer determines the mass, separating isotopes with extraordinary precision.