It has come to our attention that Figs. 3 and 4 in our recent article^{1} are incorrect. The field lines should connect up at the spherical surface. This can be shown by calculating the radial component of the field just inside the sphere [the hyperbolic field, Eq. (11)] and just outside the sphere [the Heaviside field, Eq. (17)]

Here, $r=s+(z\u2212b1+\alpha 2)z\u0302$ is the radial vector from the center of the sphere, and *r* = *αb*. Because these components are equal, the same number of field lines must exit any patch of area as enter it, and hence the field lines are continuous across the surface (though they do suffer a kink, since the tangential component is different on the two sides). As a consequence, there is no “connecting field”—or, more precisely, the connecting field carries no delta function and is irrelevant to the calculation.^{2}

A second error occurred when we quoted the field of a charge moving at the speed of light [Eq. (18)] and noted that it does not have the correct dependence on *s*—which we took to confirm the role of the connecting field. In actual fact what we have here is *not* the field of a charge moving at speed *c*, but the field of a particle moving at *close to* the speed of light adjoined to the field of a particle in hyperbolic motion (Fig. 4). In the limit, the former approaches a delta function, but to capture the strength of that delta function we must integrate the *s* component of the Heaviside field [Eq. (17)] *not* from large negative *z* to large positive *z*, but only up to the surface of the sphere, $zmax=b1+\alpha 2\u2212r2\u2212s2$; beyond that the field is hyperbolic and does not contribute to the delta function. As shown by Jerrold Franklin^{3}

In the limit *α* → *∞*,

so

which is the right coefficient [Eq. (20)], with no contribution from the connecting field.