hence

(1) |

Using Maxwell's notation, let F, G, H be the components of the vector-potential at any point; then, by 'Electricity and Magnetism,' § 616,

,
, , |

where *u, v, w* are the components of the electric current through the element *dx dy dz*, and ρ' is the distance of that element from the point at which the values of F, G, H are required, μ is the coefficient of magnetic permeability. In the case under consideration,

substituting for its value from equation (1), we get

with similar expressions for G and H.

Let us proceed to calculate the value of F at a point P.

Let 0 be the centre of the sphere; then OQ=ρ, PQ=ρ', OP = R,