Electric field outside a parallel plate capacitor

The problem of determining the electrostatic potential and field outside a parallel plate capacitor is reduced, using symmetry, to a standard boundary value problem in the half space z⩾0. In the limit that the gap d between plates approaches zero, the potential outside the plates is given as an integral over the surface of one plate. This integral is evaluated for several special cases. The magnitude of the field just outside and near the center of a two-dimensional strip capacitor of width W is shown to agree with finite difference calculations when W/d>4. The shapes of field lines outside a strip capacitor are determined, and circular lines are shown to occur near the edges. The determination of the electric field just outside and near the center of a parallel plate capacitor complements the recently published result for the magnetic field just outside and near the center of a long solenoid [J. A. Farley and R. H. Price, Am. J. Phys. 69, 751–754 (2001)].