Question

An iron rod of $0.2c{m}^2$ cross-sectional area is subjected to a magnetizing field of $1200A{m}^{-1}$. The susceptibility of iron is 599. The magnetic flux produced is:

• A. $5.43\times {10}^{-5}$ Wb
• B. $0.904\times {10}^{-5}$ Wb
• C. 0.904 Wb
• D. $1.81\times {10}^{-5}$ Wb

Answer 1

The correct option is D $1.81\times {10}^{-5}$ Wb

The permeability is given by
$\mu ={\mu }_0(1+\chi )$
Putting all values for iron rod

$\mu =4\pi \times {10}^{-7}(1+599)$

$=7.536\times {10}^{-4}H/m$
The magnetic field produced is

$B=\mu H$

$=7.536\times {10}^{-4}H/m\times 1200A{m}^{-1}$

Magnetic flux, $\varphi =\overrightarrow{B}.\overrightarrow{A}=BA\cos \theta$
Assuming field is applied perpendicular to the cross sectional area $\left(\overrightarrow{B}|\overrightarrow{|A}\right)$

$\varphi =BA=7.536\times {10}^{-4}H/m\times$

$1200A{m}^{-1}\times 0.2\times {10}^{-4}{m}^2$

$=1.81\times {10}^{-5}Wb$

Hence, option (b) is correct.