A rod of ferromagnetic material placed in a magnetic intensity \( H=5\times10^{3}\,\mathrm{A\,m^{-1}} \) acquires a magnetisation \( M=5\times10^{6}\,\mathrm{A\,m^{-1}} \). The magnetic field B inside the rod is approximately (\( \mu_0=4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6.28 T
Inside a magnetised material, the magnetic field is \( B=\mu_0\,(H+M) \). Here \( H \) is the magnetic intensity and \( M \) is the magnetisation of the material. In a ferromagnet, \( M \) is far larger than \( H \).
\( \begin{aligned} H+M &= 5\times10^{3}\,\mathrm{A\,m^{-1}}+5\times10^{6}\,\mathrm{A\,m^{-1}} \\ &= 5.005\times10^{6}\,\mathrm{A\,m^{-1}} \\ &\approx 5\times10^{6}\,\mathrm{A\,m^{-1}} \end{aligned} \)
\( \begin{aligned} B &= \mu_0\,(H+M) \\ &\approx 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}\times5\times10^{6}\,\mathrm{A\,m^{-1}} \\ &= 2\pi\,\mathrm{T} \\ &\approx 6.28\,\mathrm{T} \end{aligned} \)