Electric Field of Line Charge

The electric field of a line of charge can be found by superposing the point charge fields of infinitesmal charge elements. The radial part of the field from a charge element is given by

The integral required to obtain the field expression is

Electric Field: Ring of Charge

The electric field of a ring of charge on the axis of the ring can be found by superposing the point charge fields of infinitesmal charge elements. The ring field can then be used as an element to calculate the electric field of a charged disc.

The electric fields in the xy plane cancel by symmetry, and the z-components from charge elements can be simply added. If the charge is characterized by an area density and the ring by an incremental width dR' , then: This is a suitable element for the calculation of the electric field of a charged disc.

Electric Field:Disc of Charge