An infinitely long wire with a current `I` flowing in it is located in the boundary plane between two non-conducting media with permeabilities `mu_(1)` and `mu_(2)` . Find the modulus of the magnetic induction vector thorughout the space as a function of the distance `r` from the wire. It should be horne in mind that the lines of the vector `B` are circles whose centres lie on the axis of the wire.

Explanation

The lines of the `B` as well as `H` field are circles around the wire. Thss
`H_(1) pi r + H_(2) pi r = 1` or, `H_(1) + H_(2) = (1)/(pi r)`
Also, `mu_(0) mu_(1) H_(1) = mu_(2) H_(2) mu_(0) = B_(1) = B_(2) = B`
Thus `H_(1) = (mu_(2))/(mu_(1) + mu_(2)) (I)/(pi r)`
`H_(2) = (mu_(1))/(mu_(1) + mu_(2)) (I)/(pi r)`
and `B = mu_(0) (mu_(1) mu_(2))/(mu_(1) + mu_(2)) (I)/(pi r)`,