Analysis of the Magnetic Force Generated at a Hemispherical Microelectrode

An analytical expression is presented for the magnetic force generated during steady-state voltammetry at a hemispherical microelectrode immersed in a uniform magnetic field. Diffusion of electrogenerated ions through the magnetic field results in a magnetic force that induces convective solution flow near the electrode surface. The magnetic force per unit volume, (i.e., force density), is shown to decrease as r -2, where r is the distance away from the center of the hemispherical electrode. A consequence of the inverse square dependence of on r is that the magnetic force is confined to a microscopic solution volume near the electrode surface (e.g., ∼2 × 10-9 L for a 12.5-μm-radius hemispherical electrode). The net magnetic force acting on the diffusion layer volume, , is computed as a function of magnetic field strength and orientation and used in an approximate analysis of experimental data obtained at an inlaid 12.5-μm-radius Pt microdisk electrode. Enhancements in voltammetric currents are shown to result from magnetic forces as small as 2 × 10-11 N.