# 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?

Feb 29, 2016

Relative permeability $\setminus {\mu}_{r}$ 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 $\setminus \mu = \setminus {\mu}_{0} \setminus {\mu}_{r}$ is:

$B = \setminus \mu \left(\frac{N}{l}\right) i$

Given : B=1.63\times10^{-2}\quad T; \qquad i=0.8\quad A
$\frac{N}{l} = \frac{65}{28 \setminus \times {10}^{- 2} \setminus \quad m} = 232.14 {m}^{- 1}$

$\setminus \mu = \setminus {\mu}_{0} \setminus {\mu}_{r} = \setminus \frac{1.63 \setminus \times {10}^{- 2} \setminus \quad T}{\left(232.14 {m}^{- 1}\right) \left(0.8 \setminus \quad A\right)} = 8.77 \setminus \times {10}^{- 5} \setminus \quad \frac{T . m}{A}$

$\setminus {\mu}_{r} = \setminus \frac{\mu}{\setminus} {\mu}_{0} = \frac{8.77 \setminus \times {10}^{- 5}}{4 \setminus \pi \setminus \times {10}^{- 7}} = 688.8$

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