We show that the strength of the magnetic field in the area covered by the flare arcade following a CME-producing ejective solar eruption can be estimated from the final angular width of the CME in the outer corona and the final angular width of the flare arcade. We assume (1) the flux-rope plasmoid ejected from the flare site becomes the interior of the CME plasmoid, (2) in the outer corona the CME is roughly a "spherical plasmoid with legs" shaped like a light bulb, and (3) beyond some height in or below the outer corona the CME plasmoid is in lateral pressure balance with the surrounding magnetic field. The strength of the nearly radial magnetic field in the outer corona is estimated from the radial component of the interplanetary magnetic field measured by Ulysses. We apply this model to three well-observed CMEs that exploded from flare regions of extremely different size and magnetic setting. In each event, the estimated source-region field strength is appropriate for the magnetic setting of the flare. This agreement indicates via the model that CMEs (1) are propelled by the magnetic field of the CME plasmoid pushing against the surrounding magnetic field, and (2) can explode from flare regions that are laterally far offset from the radial path of the CME in the outer corona
