In this case the conditions given in Equation 21–12 and Equation 21–13 are not true. Assuming that the electrical conductivity of the media in which field is generated is the same as that of the flow, that is , from Equation 21–9 and Equation 21–11 the induction equation can be written as:

(21–16)

and the current density is given by:

(21–17)

For the induction equation Equation 21–14 or Equation 21–16, the boundary conditions for the induced field are given by:

(21–18)

where the subscripts denote the normal and tangential components of the field and is specified by you. For an electrically insulating boundary, as at the boundary, from Ampere’s relation one has at the boundary.