We study the conformal data of a generic superconformal line defect preserving half of the supercharges in a four-dimensional N=2 conformal theory. We prove a theory independent relation between the one-point function of the stress tensor in the presence of the line defect and the two-point function of the displacement operator. When the defect is interpreted as a heavy charged particle in a gauge theory, the result relates the energy emitted through bremsstrahlung with the coupling of the stress tensor to the particle at rest.