A new crossed-beam scattering apparatus "Perfectron" requires a uniform magnetic field to realize its perfect focusing property in combination with a three dimensional quadrupole electrostatic field. As is well known, a spherical air-core coil produces a uniform magnetic field (in the z axis) within its whole domain. The strength of the magnetic field B (in gauss) is given by B = (4π/15) NzI, where Nz and I denote the number of winding in turns/cm in the z axis and the exciting current in Ampere. We have, therefore, constructed a large spherical coil of about one meter in diameter, inside which a whole scattering chamber is housed. The coil is designed to provide the maximum magnetic field of 650 gausses with water-cooling and 250 gausses without water-cooling. A deviation of the magnetic field caused by coil imperfections which are compelled to do so from experimental requirements is also designed to be less than 0.5 % in the central region of the coil.