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The beam-helicity asymmetry has been measured simultaneously for thereactions (e p \to e p \gamma) and (e p \to e p \pi^0) in the $\Delta (1232)$resonance region at $Q^2=$ 0.35 (GeV/c)$^2$. The experiment was performed atMAMI with a longitudinally polarized beam and an out-of-plane detection of theproton. The results are compared with calculations based on DispersionRelations for virtual Compton scattering and with the MAID model for pionelectroproduction. There is an overall good agreement between experiment andtheoretical calculations. The remaining discrepancies may be ascribed to animperfect parametrization of some $\gamma^{(*)} N \to \pi N$ multipoles, mainlycontributing to the non-resonant background. The beam-helicity asymmetry inboth channels ($\gamma$ and $\pi^0$) shows a good sensitivity to thesemultipoles and should allow future improvement in their parametrization.Comment: 7 pages, 8 figures, version to appear in EPJ

Beam-helicity asymmetry in photon and pion electroproduction in the Δ(1232)-resonance region at Q2 = 0.35(GeV/c)2