The calculation for α = 2, 3 (force components in the y and z directions) yields similar results, so collecting the 3 equations into one: d p d τ τ = q γ γ ( E + v × × B ) , and since differentials in coordinate time dt and proper time dτ are related by the Lorentz factor, d t = γ γ ( v ) d τ τ , so we arrive at d p d t = q ( E + v × × B ) .