Question

A rod of ferromagnetic material with dimensions $10cm\times 0.5cm\times 0.2cm$ is placed in a magnetic field of strength $0.5cm\times {10}^{4}A{m}^{-1}$ as a result of which a magnetic moment of $5A{m}^{-2}$ is produced in the rod. The value of magnetic induction will be

• A. $0.358$ T
• B. $0.54$ T
• C. $6.28$ T
• D. $2.519$T

Answer 1

The correct option is C $6.28$ T

Here, $V=10\times 0.5\times 0.2c{m}^3={10}^{-6}{m}^3$
$H=0.5\times {10}^{4}A{m}^{-1}=5\times {10}^{3}A{m}^{-1}$
$M=5A{m}^{-2};B=?$
$I=\frac{M}{V}=\frac{5}{{10}^{-6}}=5\times {10}^{6}A{m}^{-1}$}
$B={\mu }_0(H+I)=4\pi \times {10}^{-7}(5\times {10}^3+5\times {10}^6)=6.28T$