What does the electric field look like emanating from a tesla coil?

The magnetic field from a wire wraps around it. The direction depends on the direction of the current. This means that the magnetic field passes through the center of the secondary coil, then out each end, and around the coil.

But a Tesla transmits a large electric field. If the electric field is orthogonal to the magnet field, does this mean that the electric field emanates directly out, perpendicular to the the length of the coil and that of the wire?