Question

A copper wire is wrapped 65 times around an unknown core of length 28cm. The current in the wire is 800mA and the magnetic field due to the electromagnet is 1.63 x 10-2T. What is the most likely material the wire is wrapped around?

Answer 1

Relative permeability `\mu_r` is 689 which is closer to the value for Manganes-Zinc Ferrite. So the core is likely made of Manganese-Zinc Ferrite.

Explanation:

Solenoid: The magnetic field strength `B`, inside a solenoid of length `l` made of `N` number of turns, carrying a current `i` and having a core made of a material with magnetic permeability `\mu=\mu_0\mu_r` is:

`B = \mu(N/l)i`

Given : `B=1.63\times10^{-2}\quad T; \qquad i=0.8\quad A`
`N/l = 65/(28\times10^{-2} \quad m)=232.14m^{-1}`

`\mu = \mu_0\mu_r = \frac{1.63\times10^{-2}\quad T}{(232.14m^{-1})(0.8\quad A)}=8.77\times10^{-5} \quad (T.m)/A`

`\mu_r = \mu/\mu_0 = (8.77\times10^{-5})/(4\pi\times10^{-7})=688.8`

Manganese-Zinc Ferrite has a relative permeability of around 640 (according to wikipedia) . So it could be a Manganese-Zinc Ferrite core. Thanks to Miroslav and A08 for correcting me here.

Magnetic Properties of Materials Reference: https://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29