Question

A magnetic field of $1600A{m}^{-1}$ produces flux of $2.4\times {10}^{-5}$ weber in a iron bar of the cross-sectional area of $0.2c{m}^2$. The permeability of the iron bar is:

• A. $245$
• B. $250$
• C. $252$
• D. $597$

Answer 1

The correct option is D $597$

Given,

$H=1600A{m}^{-1}$, $\varphi =2.4\times {10}^{-5}weber$, A$=0.2c{m}^2$

$\frac{\varphi }{A}=B=\mu H$

$\Rightarrow B=\frac{\varphi }{A}=\frac{2.4\times {10}^{-5}}{0.2\times {10}^{-4}}\times \frac{weber}{m^2}$

$=0.12T$

$\mu =\frac{B}{H}=\frac{0.12}{1600}=7.5\times {10}^{-4}T{A}^{-1}m$

$\Rightarrow {\mu }_r=\frac{\mu }{{\mu }_w}=\frac{7.5\times {10}^{-4}}{4\pi \times {10}^{-7}}$
$\Rightarrow {\mu }_r=597$
Hence, the correct option is $\left(D\right)$