B.3 For wires in poloial plane

For a curve in the poloidal plane, the line element dl in terms of the cylindrical basis is written as dl = dRˆeR(ϕ) + dZˆez. Using Cartesian coordinate basis vectors, dl is written as

dl = dR cosϕˆex +dR sin ϕˆey + dZ ˆez.
(632)

Using Eq. (632) and (626), we obtain

            ||   ˆex     ˆey     ˆez  ||
dl× (r − r′) = ||dR cosϕ dR sinϕ dZ   ||.
            ||(x − x ′) (y − y′) (z − z′)||
(633)