The impact parameter b is the perpendicular offset of the trajectory of the incoming particle, and the outgoing particle emerges at an angle θ. For a given interaction (coulombic, magnetic, gravitational, contact, etc.), the impact parameter and the scattering angle have a definite one-to-one functional dependence on each other. Generally the impact parameter can neither be controlled nor measured from event to event and is assumed to take all possible values when averaging over many scattering events. The differential size of the cross section is the area element in the plane of the impact parameter, i.e. d σ = b d φ d b. The differential angular range of the scattered particle at angle θ is the solid angle element dΩ = sin θ d θ d φ. The differential cross section is the quotient of these quantities, ⁠ d σ / dΩ ⁠.