2.2.2 Case 2: $\vec{B_0}$ Generated in Conducting Media

In this case the conditions given in Equations  2.2-6 and 2.2-7 are not true. Assuming that the electrical conductivity of the media in which field $\vec{B_0}$ is generated is the same as that of the flow, i.e. $\sigma{'}=\sigma$, from Equations  2.2-3 and 2.2-5 the induction equation can be written as:

and the current density is given by:

For the induction equation Equations  2.2-8 or 2.2-10, the boundary conditions for the induced field are given by:

where the subscripts denote the normal and tangential components of the field and $\vec{b^*}$ is specified by the user. For an electrically insulating boundary, as $j_n=0$ at the boundary, from Ampere's relation one has $b_{\rm t1} = b_{\rm t2} = 0$ at the boundary.