Magnetic Force Calculator

The magnetic force on a moving charged particle is given by the Lorentz force law:

$$\vec{F} = q\vec{v} \times \vec{B}$$

The magnitude is $$F = qvB\sin\theta$$, where θ is the angle between the velocity vector and the magnetic field vector. Key features:

• The force is maximum when v ⊥ B (θ = 90°) and zero when v ∥ B (θ = 0° or 180°).
• The force direction is perpendicular to both v and B, determined by the right-hand rule (for positive charges).
• Because the force is always perpendicular to velocity, it does no work — it changes direction but not speed.

For a straight wire of length L carrying current I in a uniform field B:

$$F = BIL\sin\theta$$

When the wire is perpendicular to the field (θ = 90°), this simplifies to $$F = BIL$$. This is the principle behind electric motors, where current-carrying coils experience torque in a magnetic field.

The direction of force on a wire follows the same right-hand rule: point fingers from current direction toward B, and the thumb gives the force direction. For negative charges (electrons), the force direction reverses.

The calculated force tells you the magnitude of the magnetic force in newtons. For charged particles, this force causes circular motion with radius $$r = \frac{mv}{qB}$$. For wires in motors, the force produces torque. Note that if θ = 0° (particle moving parallel to the field), the force is zero — the magnetic field only deflects particles with a velocity component perpendicular to it.