Question

A rod of ferromagnetic material with dimension $10\times 0.5\times 0.2c{m}^3$ is placed in a magnetic field of strength $0.5\times {10}^{4}A{m}^{-1}$ as a result of which a magnetic field of $5A{m}^{-2}$ is produced in the rod. The value of magnetic induction will be

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

Answer 1

The correct option is C $6.28T$

Magnetization $I=\frac{M}{V}$

Magnetic induction $B={\mu }_0(H+I)={\mu }_0(H+\frac{M}{V})$

Given : $V=10\times 0.5\times 0.2c{m}^3={10}^{-6}{m}^3$, $M=5A{m}^{-2}$ and $H=0.5\times {10}^{4}A{m}^{-1}$
$\therefore$ $B=4\pi \times {10}^{-7}(.5\times {10}^4+\frac{5}{{10}^{-6}})=6.28T$