Experimental investigations on the RECE‐Berta device at Cornell show that weak gradients in the applied magnetic field do not influence the stability of strong relativistic electron rings for field differences across the rings of up to 0.8%. The main effect of such gradients is a radial displacement of the equilibrium position of the rings toward the low‐field region of the tank. The magnitude of this displacement depends on the field gradient, and the strength and geometry of the electron ring. A theory for the displaced electron ring equilibria is presented which assumes a balance of the forces due to the external field and the image fields arising from currents in the conducting tank wall. The theory shows good quantitative agreement with the observed ring movement. From these results it appears that the final “dump” of the rings can be explained by the existence of a gradient in the basic mirror field.