Biot-Savart equation not behaving as expected I am currently in the process making a large electromagnet with a permeable core that has the following specs:

*

*I = 250A

*N = 300

*L = 0.25m

*relative permability of core = 230000

$B=\frac{\mu_r \mu_0 NI}{L}$
When I plug these values into the above equation, I get 86350 Teslas, which I am certain cannot be correct. Am I using this equation incorrectly?
 A: Magnetic cores experience saturation: the magnetization of the material (which is what reinforces the $\mathbf B$ field) increases in proportion to the applied field only up to a limit, at which point the proportionality ceases to hold.
Effectively, the relative permeability of your material is only 230000 for low values of $H=\frac{IN}L.$ You can see this on the magnetization curve for your material. Wikipedia has one for a few common materials. The relative permeability you quote is the slope of this curve near the origin. Far from the origin, the slope flattens out greatly and $B$ no longer grows nearly as quickly with $H.$ Unless you are given a corrected value of $\mu_r$ for the high field regime, the equation $B=\frac{\mu_r\mu_0NI}L$ is not particularly useful and you should be directly referencing a magnetization curve.
Pure iron has a similar relative permeability (around 200000) at low fields. However, looking up its magnetization curve shows that it will actually top out at around $B\approx1\,\mathrm{tesla}$ at your value of $H.$
