What do the magnetic fields lines produced by a solenoid made out of another solenoid look like?

Suppose we take a solenoid:

I was wondering what the magnetic field pattern would look like if the black current-carrying wire in the depicted solenoid was replaced by a solenoid. In other words, what would the magnetic field pattern look like if we made a solenoid out of a current-carrying solenoid instead of out of a current conducting wire? This is not the same as a toroid:

I can imagine how the field pattern comes to be if we curl up a straight current-carrying wire to make a (multiple winded) solenoid, but I find it hard to imagine what pattern emerges if we curl up a (multiple winded) solenoid. For a toroid the situation is clear.

But the situation is different for the kind of solenoid I described. The field lines that enter (or leave) the solenoid at one side, leave (or enter) the solenoid on the other side. This means that the in- and outgoing magnetic field lines (the north and south pole) must be connected.

For simplicity, let's assume that the two ends of the solenoids are parallel. Will the field inside this solenoid be the same as in a toroid? Outside of the solenoid, at least as far as I think, doesn't there has to be a magnetic field pattern also? Going in (out) on one side of the solenoid and out (in) on the opposite side, Continuing the field inside and making a closed pattern of field lines?

• Curl up a solenoid. Are you talking about a toroid? You should definitely post a diagram depicting your shape. Jan 7, 2019 at 16:17