A novel technique has been developed which allows a quadratic magnetic field to be continuously varied (via a superconducting flux transformer) from the outside of an ultrahigh‐vacuum container placed within a superconducting solenoid. Enclosed within each of these vacuum vessels is a high‐precision (compensated) Penning trap which is used in a variety of geonium experiments at the University of Washington. By varying the dc current in an outer (normal) primary solenoid, the secondary current flowing within a shorted superconducting loop is varied accordingly. The superconducting loop need only be placed in a cylindrically symmetric position within the Penning trap in order to generate theB2term, and with a clever choice of geometry, the zeroth‐order term can be totally eliminated. As an additional highlight, the uniform field from the main solenoid is drift stabilized to the same degree as the basic cancellation and further, an auxiliary trim coil can be used to fine trim the zeroth‐order null.