See Magnetic Forces and Fields for a discussion on this. For a coil with a shape factor of 1, very typical of induction coils, Equation (7) indicates that the coil will have only 69 of the z-component magnetic flux. A similar application of the magnetic field distribution created by Helmholtz coils is found in a magnetic bottle that can temporarily trap charged particles. Helmholtz coils typically have loops with equal radii with current flowing in the same direction to have a strong uniform field at the midpoint between the loops.
