Question

A material core has 10 turns per $\text{cm}$ of the wire wound uniformly upon it , which carries a current of $2.0\text{A}$. The flux density in the material is $1.0{\text{Wb/m}}^2$. The relative permeability of the core is:

• A. $245$
• B. $397$
• C. $450$
• D. $175$

Answer 1

The correct option is B $397$

We know that,

$H=nI$

$\text{No of turns per unit length}$

$n=\frac{10}{{10}^{-2}}=1000$

$H=1000\times 2=2000\text{A/m}$

Now, $B=\mu H$

$\Rightarrow \mu =\frac{B}{H}=\frac{1}{2000}=0.5\times {10}^{-3}$

Now, Relative permeability is given by,

${\mu }_r=\frac{{\mu }_m}{{\mu }_o}=\frac{0.5\times {10}^{-3}}{4\pi \times {10}^{-7}}=397$