A toroidally localized vertical magnetic field produced by an external coil (the 'n = 1 coil') is applied to a rotating tokamak plasma driven by co-injected tangential neutral beams and in the high confinement H-mode. The toroidal plasma rotation is greatly slowed by magnetic braking, with consequent reduction and reversal of the core radial electric field E(r) and the shear in E(r); the plasma maintains a negative edge E(r) and a negative edge E(r) shear, despite the large core changes, and remains in the H-mode with insignificant changes in global confinement, density profile and temperature profiles. The experimental observations are consistent with theories predicting that the high confinement H-mode is produced and maintained by an edge region where strong radial shear in the velocity, v(perpendicular-to)over arrow pointing right = E(r)over arrow pointing right x B(over arrow pointing right)/B(over arrow pointing right).B(over arrow pointing right), suppresses density microturbulence and resultant transport loss, and that in regions where the radial shear in v(perpendicular-to) almost-equal-to E(r)/B(phi) is below a critical value for turbulence quenching, as in the core of DIII-D, large core changes (reductions) in rotation, E(r) and shear in E(r) have no effect on confinement.