Your design team is working on an air-core toroid that is to have the greatest feasible magnetic field per ampere of current but in which the greatest magnetic field magnitude must be exactly four times the smallest magnetic field magnitude. Because of space and cost restrictions, the maximum length of wire you can use is \(100 \mathrm{~m}\) and the core radius must be at least \(30 \mathrm{~mm}\). You begin to speculate about how many turns the toroid needs to have, its inner and outer radii, and how much magnetic field you might achieve.