Abstract: Based on discussing for the problem of magnetic field inside an ellipsoidal coil, this paper employs a numerical method to calculate the magnetic field inside several different shapes of coil. Using the same way to wind the coil on ellipsoid, paraboloid or hyperboloid, we find that the magnetic field inside can be uniform. The general formula is also confirmed. Possible ways to generate a large space of uniform magnetic fields are provided.

Key words: uniform magnetic field, numerical calculation, ellipsoidal coil, paraboloidal coil, hyperboloidalcoil, quadric surface coil