Lorentz Force — Magnitude

Scalar form where θ is the angle between v and B. Maximum when v ⊥ B; zero when v ∥ B.

Scalar Form

From $\vec{F} = q(\vec{v} \times \vec{B})$, the magnitude:

$$\boxed{F = qvB\sin\theta}$$

where $\theta$ is the angle between $\vec{v}$ and $\vec{B}$.

Limiting Cases

Units

$$[F] = \text{N}, \quad [B] = \frac{\text{N}}{\text{A·m}} = \text{T (tesla)}$$

One tesla is the field that exerts 1 N on a 1 C charge moving at 1 m/s perpendicular to the field.