All Problems

Constant Magnetic Field, Magnetics

Problem 3.277

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 throughout the space as a function of the distance \(r\) from the wire. It should be borne in mind that the lines of the vector \(B\) are circles whose centres lie on the axis of the wire.

Reveal Answer
B=μ0μ1μ2μ1+μ2IπrB=\frac{\mu_{0} \mu_{1} \mu_{2}}{\mu_{1}+\mu_{2}} \frac{I}{\pi r}